W- 0 0 d$ We NV.
I
set
following matrix form
ACAX 4 BY + Cz t1)
EN
d
[A3IX1 s [hj (14: Xszx-
7 2 =
à t£ B^ CF
where [A] is the coefficient matrix which
Contain eno initial values of the - B(AX * BY + cE_+ 1)
; : Y yx E (18)
2 2
s oF, or, oF, A" * B" + c?
( 3% uw rn ( 1]
ar av ac CCAX + By t CZ * 15
> > 4, = a i = T
8E. A". B^. C^
—3
(Ai = ab To find the coordinates of p(x ,y )in I,
= 2 e
: it is necessary to rely on st legst two
: image points, e.g. B and a,, whose space
ôF, i3 and image plane coordinates are known.
{ ; ( 2
T j e ^ ‘ e
| ox e aC ] The space coordinates ay (X 2424) and
= 4 4 P4
85(X,, Y,,Z,)can be found‘ from (6) and
[X] is the unknown vector where C While the image plane coordinates
m B4 Ou y4 7 and an (Xp; Yo} are originally
[X] = [dY ,dY.,47 ‚dA,dB,dC], and : : :
a s S given. As shown in Fig. (2 the
[B] is the constant term vector lengths of the line segments 11,15 and 14
Toro 5 Es = are given by 2 :
[B] =[ LET (Fol, sieve = (F o1; *hose
components are found by substituting the
initial values in (9). (
,1P V 3
2 sl
Equation (14) are solved to obtain
corrections dX _,dY_, et + ac. These
corrections are added to M eot eo? 4e C.
to obtain improved estimates and the
procedure is continued until the
corrections are negligible. It is to be
noted that the iteration problem is
convergent if the initial values are near
the solution (similar to Newton's method
for solving & system of nonlinear Fig. (2)
equations).
Determination of the Focal Length £f and
: 2 2 — V z 2 ^ « 2 ; - - 2
the Principal Point p 1,58 p= Kx -x^ S +02 =.)
After determining the six external l.:R.p = P XY x Y IL lY. (17)
( Y nn A BU 271 eo 07345 791 lel
orientation elements (X a.c BQQUPE >, - rr : 5 : 5
the focal length can be calculated as the 139 794997 ART} f UESUE.
length of the perpendiculsr dropped from 5
onto H and is given by
The sispe of a,s,in
| AX. € BF, + Un 4 1 | The slope of &,851n
E = = = S (15) -
y y
2 2 20-5 2 À 18)
A ra + CF) Lan ow 7 NI X1 (um
The space coordinates of the principal The angle 8 = « Pa, a can be found from
point p(X,, Y,,Z Jean be found as the the cosine law : 2 2
e
point of intersection of the just cos 0 = 15 * 15 1, (19)
mentioned perpendicular with the image = E: 211
plane M as follows : 2 3
399
