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The adjustment is thus reduced to the simple case of indirect observations With ¢
weight. From the available condition-equations (5) the 5 normal equations are EM
Their solution together with application of the equations (4) gives the adjusted -
of the elements of relative orientation. i
The relative orientation is followed sy scaling of the model to the pr
The heights of two or more common points are computed in both model
of corresponding rays and an average value for the scale is determined.
Following the orientation of the photographs of a strip,
measured points are computed from the equations of the
These equations read:
eceding on.
s by intersecting
strip co-ordinates of the
rays through corresponding Points
X Y Z (0)
in which the subscript O, refers to a projection centre.
This computation also reveals the remaining parallaxes in these poinfs, The possi.
bility of checking the accuracy of the triangulation is thus provided.
Finally the strip co-ordinates are transformed to the terrestrial or map co-ordinate
system using the ground control points. Two ground control points with known plane qv.
ordinates are necessary and three ground control points of which heights are known, This
transformation requires a scaling of the strip, three rotations about mutually perpendicular
axes and three translations in mutually perpendicular directions. The transformation
formulas that achieve this can be derived from the equations (2) by adding a scale factor
and a constant to the second parts:
X = À (Lx + Ly +02 ) + 6x
Y =) (myx + my + mz) 4- ey (7)
Z =] (nu + ny + nz) +c,
In these formulas x, ¥ and z are now strip co-ordinates and X, Y and Z are terrestrial
co-ordinates.
These formulas are again non-linear in the rotations. Let x, y and z be subsituted by
co-ordinates Xj, Yi and Zi, obtained from the equations (2) by substitution of approximate
values for the rotations. Differentiation of the formulas (7) and first order approximation
then gives:
X = Xi liv1 -- JZidg — Yi dz -- eui
Y — Yi j1— JZido + 17 Yi da E eyit1 (8)
Z = 217351 + 1 Yido— A Xi dp+ ezi+1
The two ground control points with known plane co-ordinate produce two equations (8)
of the first type and two of the second type. The three ground control points of known
heights produce three equations of the third type. In these seven equations occur ap-
proximate values of the required scale factor, rotations and translations. Solution of these
equations results in better approximations. Those for the scale factor and the translations
follow immediately from the equations. Those for the rotations are, as before, found by
multiplying determinants of direction cosines, using equation (4).
As initial approximations estimated values may be chosen. Improved approximations
are computed with the equations (2), (8) and (4) and in their turn substituted into the
equations until the corrections obtained are negligible. The final values are substituted
in the equations (7) and the strip co-ordinates of all points are transformed.
Experiments.
This triangulation procedure has been coded and tried out on two examples.
The first example is a theoretical one. It consists of a strip of 11 photographs. Al
photographs are exactly vertical and flown in a straight line. Each base is 3 km, giving
a total Jen
rigid rect
initial Phe
system the
were used
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horizontal
| mm.
This €
ation usin
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A third
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for each pa
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alibrated c
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This wk
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that remain
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