Image Processing Reference
In-Depth Information
Fig. 13.4. The checkerboard consists of black and white squares with side lengths of 28 mm.
Such patterns are frequently used to calibrate cameras, i.e., their intrinsic and extrinsic param-
eters are computed
When m , and thereby M , is estimated, however, M I and M E are yet to be
determined. To do that, we spell out M in terms of its physical parameters.
f x
0
c 0
R 11 R 12 R 13 t X
R 21 R 22 R 23 t Y
R 31 R 32 R 33
M =
0
f y r 0
001
(13.63)
t Z
f x R 11 + c 0 R 31 ,
f x R 12 + c 0 R 32 ,
f x R 13 + c 0 R 33 ,
f x t x + c 0 t z
=
f y R 21 + r 0 R 31 ,
f y R 22 + r 0 R 32 ,
f y R 23 + r 0 R 33 ,
f y t y + r 0 t z
R 31 ,
R 32 ,
R 33 ,
t z
Accordingly, and by observing that the first three columns of the last row in M is a
row of an orthogonal matrix that should have the norm 1 [70], we can compute first
γ
M 31 + M 32 + M 33 = γ R 31 + R 32 + R 33 = γ
(13.64)
and normalize M as
1
γ M
M
(13.65)
Next we calculate c 0 ,r 0 ,f x ,f y by building pairwise scalar products between the
subrows of Eq. (13.63) that contain the elements of R to conclude that
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