International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
where A= (a X, +h.Y +e, Zz)
From formula (4), (5), (6), (7), then:
(^, - hyx,) 29
f À
(^. - hx.) 9 b 5
J A
A
(hs da eh 6
f nde
LE utt
A (10)
e
From formula (8), (9), (10) to reduce the parameter À , and
a,b, + a,b, + azb, = 0, then:
(A, ri )(A, -hx). (A, a jJ Vs hos) pp =0 01)
fs 2
f - —h,x,)-(h -hx,)- Us - hys). - hys) (12)
hh,
Considering the primary point (xo, yo) close to the centre of the
image, the initial value of focus f is able to be computed on the
assumption that the primary point is in the centre of the image.
At present the initial values of the intrinsic parameters of the
projector f, xo, yo have been gotten from the formulas above.
Then the initial values of the extrinsic parameters of the
projector (6,0, K, XY ui) are deduced from the next
formulas.
From formula (8) and (10), and from the formula (9) and (10),
then:
a pan b (a hx (13)
b,
a; fh, fh,
e s. UT T h, y.) > S (dav) pr
es Jh, Jh;
Angle K is able to be calculated from the formula (15).
UAMBNC OY al
foK mtm (15)
io ph s
From the formula (13), (14), and b; + b; + bi = |, then:
2 1
(A, — IX, E " (^; — Its y y
Pu C FA
=
La
Il
(16)
1+
Angle @ is able to be calculated from the known angle Æ and
the formula (17).
sina z nb (17)
Angle Ó is able to be calculated from the known angle XK,
angle @ and the formula (18).
gp = i , 18)
s abre A, 5 023;
2
qui tes.
From the formula (8), (9), (10) and (6), then:
hy = x, Lax, tb, ez.
hs = y, Lax, +b,Y, +c,Z,) am
A = (a; X, th}, +c;Z,)
The initial values of X. 2 y > Z. are able to be calculated from
the formula (19).
So, the initial values of the intrinsic and extrinsic parameters of
the projector can be worked out from the deduction above.
Because the distortion is sure to exist in the projector lens, the
distortion parameters of it should be worked out in the process
of the projector calibration.
Internat
The dis
then:
X—X 7
m
where
From th
The fori
finally.
