Calibration. Dorit Moshe. In today’s show. How positions in the image relate to 3D positions in the world? We will use analytical geometry to quantify more precisely the relationship between a camera, the objects it observes, and the pictures of these objects
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Markus Raetz, Metamorphose II, 1991-92
a point O in E3 and three unit vectors i, j and k orthogonal to each other
f is a distance in meters
3 coords of t
3 raws of R
M is only defined up to scale in this setting!!
And we get
Relation between image positions, u,v to points at 3D positions in P (homogenous coordinates)
Which features should we choose?
There is no single solution if n≥p. The non trivial solution exists only if A is non singular.
We will try to find vector x that minimize E (the error measure):
e1 minimizes the error E. It is the eigenvector associated with the minimum eigenvalue of ATA (λ1 )
Projection of each point gives us two equations and there are 11 unknowns. 6 points in general position are sufficient for calibration.
We take as input a set of at least 6 non-coplanar 3D anchor points, and their 2D images. The 2D coordinates do not need to be very accurate, they are typically obtained manually by a user who clicks their approximate position.