of the right camera of the first model (1,0,0) and
the unit of length should be the base length of
the second model. lt is of course that the base
direction of the second model should be on the x-
axis of the coordinate sysem.
Thus, for adjacent two models, relative orienta-
tions are made independently, always referring to
the common coordinate system fixed in space.
And as a result of this method the space orienta-
tions of their common photograph become different.
This enables us to give the first model the three
dimentional rotation and the scale transfer, so as
the space ortentations of their common photograph
should coincide with each other, 1) transferring
its coordinate origin to the projection center of
the right camera of the first model, 2) determining
the scale factor, 3) rotating the first model about
the new origin in the order —«,'?, —4,'», —«,»,
cosq, ? 0 —sing,? cos «,'? sin«,?? 0| cos«,? —sin«,'? 0 | Cosgp:V” 0sings ? [1 0 0 |
0 1 0 —S$in «,'? cosæ, ‘? 0 | Sin, cosk, V0 0 1 0 0 cose," sino," (14)
sing, ? 0 cose, ? | 0 0 1l] +0 0 1| — sing» 0 cosq,'" | 0 — sine,” cose," |
where the rotational direction of coordinate system
is taken as that of Jerie.
It must be noted that a peculiar charasteristic
of this succesive orientation is at the point that,
not as usual, the connection of models are followed
from begging to end in order that the new origin
of coordinate system should not be moved, until
the rotation and the scale transfer of the model
will be finished. Consequently, it is obvious that,
when succesive orientation of a strip has been
completed, the strip coordinates are being referred
to the coordinate system of the last model and
expressed by its base distance.
5. Pure-analytical method.
5-1. We have mentioned in article 2 about the
method in which only the absolute orientation is
executed by computation, calling it semi-analytical.
Instead of orientation by A7, we can make relative
and succesive orientation by computation as shown
in article 3 and 4. For absolute orientation the
same method will be applied as in article 2-1. In
this case we called the method pure-analytical.
The example of pure-analytical method will be
presented below.
5-2. Analytical aerial triangulation of grid
plates.
lf photographic coordinates (x, y) of corners of
a grid plate are measured on one of the camera
of Autograph AT7, giving some value for «, «, and
o, respectively with constant f and z, then it is
equivalent to have photographed the accurate
mesh on the ground with some rotation and incli-
nation of the camera. Let us make the another
measurement of a grid plate with different x, @
and c, and we obtain a stereo pair of photographs
of a accurate mesh on the flat ground with some
K1?7, q,?, where 0, is a measure relating to the
second photograph of the first model and so on;
The formula for the above three processes are
as follows ;
1) Transfer of origin
AA, y R2 (12)
2) Scale transfer,
lur
m n e i (13)
IA | G9 yhp Cr 9 yr (2,2)? y mu
\ (x:P)E4 (y; 9934 (2, 9)? WEN
where r; is the vector length of common points
in two adjacent models,
3) Rotation,
Rotational matrix of the first model to connect
it to the second model is obtained by matrix
multiplication,
(1)
different inclination and rotation of the camera.
Such a combination of some photographs con-
structs an ideal strip. Results of analytical aerial
triangulation for such a strip is as follows,
Condition.
1) Equivalent focal length of camera 150 mm.
2) Accuracy of grid plate «10,4. (made by Wild)
3) Length of the strip 10 models.
4) Fleight-height base ratio 1. 875
5) Equivalent base length 1 km.
Results.
1) Residual parallax in the mean 2.54
2) Mean discrepancies at common points of
adjacent models
x y z
upper point 1 39 (+39) 57(+46)
middle point 1 10(+ 1) 22(— 7)
lower point 1 31(+4+31) 54( — 46)
Unit is 0.00001 of base length, and the values
shown in bracket are the means made under
consideration of signs.
From the above results, we may see that the
discrepancies at pass points are correspondingly
large and systematic.
3) Residual errors at the corners of the grid
are shown in following diagrams. Bending of a
strip in (x, y) plane which amounts to 10 to 20 m.
of deviation at one end of the strip, as shown in
fig. 2, is corrected by conformal transformation
as in fig. 3 and fig. 4. In the first case, 6 control
points are used for the transformation (fig. 3),
and in the second case, the minimum control points
(3 points) are used for the same purpose, (fig. 4).
Frequency curves of errors corresponding to the
above two cases are shown in fig. 6. Analogous
expressions for the residual errors of z are in
fig. 5 and 6.
