Figure 7: Space coordinates of So
3.7 The Camera Station S
1.
. The line
The equation of the perpendicular n dropped
from Sy onto t is:
X X0
or in space
(X — Xk)cos x + (Y — Yx)sinx = Xso (28)
Equation(28) represents also a plane v perpen-
dicular to a through S and Sp [1].
It is known that points lying on the same ray
through S have a common image. Let T € a bea
point whose image coincides with A$(l : tj : t5).
The points T' € o and As in space should lie on
the same ray (see fig.(1)).
The Spac coordinates of T(Xr,Yr) can be de-
termined using the equation (3), then (17a), and
(18a).
through As(Xs,Ys, Zs) and
T(Xr,Yr,0) have the parametric equation:
Xvo= oXgph it (Xr — Xs) t
Y = Yr + (Yr-Ys)t (29)
7 = — Js t
Substituting into(28), the value of the parameter
t, for the camera station S can be determined.
When ts is substituted for t into (29) the coor-
dinates (Xs, Ys, Zs) can be found.
. As a check, the distance between S and the van-
ishing line v can be calculated and compared to
r, deduced from(27). This means that the five
control points and their images are subject to a
certain constraint.
3.8 Determining the rest of the Orientation
Parameters
1
The position of S(Xs,Ys, Zs) and the angle x
have already been found. The rest of the pa-
rameters depend on knowing the position of the
6
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
image plane 7 in space. It is the plane containing
t, parallel to the plane through S and v.
Let the direction ratio of its normal vector n be
(m, n, l), then
i i f
mitnitl!-| Xvi—- Xs Yvi-Ys -—Zs
Xk — XL Yk-Yr 0
(30
hence:
m - Zs(íYk-—Yr)
n = -—Zs(Xk - Xr) (31)
(Xvi — Xs)(Yx — Yr)
T(Yvi-Ys)Xk — Xr)
from which the equation of v has the form:
m(X — Xg)+n(Y —=Yg)+1Z2=0 (32)
2. The parametric equation of the normal vector n
will be:
= As 4. mt
Y ziYs b: nt (33)
Z = 23; + ll
which, when substituted into(32) yields the val-
ue t, for the parameter ¢ corresponding to the
central point P', hence its coordinates will be:
Xp mu Xg.H m tp
‘pr = Ys + n tp (34)
Zp: = Zs +3 tp
Finally the focal length f = SP’ and the angle
w (between m and «) are found to be:
f2vm -trn?-4P t,
l
Q — arccos( ———————— ).
m? + n? + 12
4. RECONSTRUCTION OF SPACE MOD-
ELS
A space point lies at the point of intersection of the
corresponding pair of rays connecting each station po-
sition to the image of that point. After determining
the orientation parameters of a camera and the space
coordinates of the camera stations(S;, S,) for both
photos(left and right) (see fig.(8)), the space coordi-
nate of the intersection point of two corresponding
rays can be determined as follow:
1. Let Ae, be a point in a, whose image is A. ( in
right photo). Its homogeneous coordinates can
be found easily by using equation(3). Then the
space coordinates can be calculated as mentioned
previously. Similarly, the space coordinates for
point A,,, whose image is A; (in left photo) can
be calculated.
Figure 8: Sp.
tos
2. The spa
point o
Sr Aa
re
These steps
of both S; a
the space mc
be all calcul:
However, du
responding r
shortest dist
space point .
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6. ACCUR
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