Camera Calibration class 9. Multiple View Geometry Comp 290-089 Marc Pollefeys. Multiple View Geometry course schedule (subject to change). Single view geometry. Camera model Camera calibration Single view geom. Pinhole camera. Camera anatomy. Camera center Column points
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Multiple View Geometry
Single view geom.
absorb d0 in K2x2
alternatives, because 8dof (3+3+2), not more
principal point is not defined
Scaled orthographic projection
Weak perspective projection
Straight lines are not mapped to straight lines!
(otherwise it would be a projective camera)
Null-space PC=0 yields camera center
P has 11 dof, 2 independent eq./points
n 6 points
(i) Simple, as before
(ii) Anisotropic scaling
Extend DLT to lines
(2 independent eq.)
Errors in the image and in the world
of algebraic error
note invariance to 2D and 3D similarities
given proper normalization
note that in this case algebraic error = geometric error
Calibrated camera, position and orientation unkown
6 dof 3 points minimal (4 solutions in general)
ML residual error
Example: n=197, =0.365, =0.37
Compute Jacobian at ML solution, then
(variance per parameter can be found on diagonal)
=distribution of sum of squares)
short and long focal length
Choice of the distortion function and center
planes, lines, conics and quadrics.