2.3 Analytical aerial levelling (S3)
This step can start as soon as one model is measured. It consists of
doing, analytically the dependent relative orientation of all the
photos of the strip (except the first). Gross errors are searched
for, at the adjustment of every new model connected to the segment
of strip. The size of the errors detectable at this phase is much
smaller then the previous ones. Errors between 3 and 100 standard
deviations can be removed at this phase. At points commom to two
models, even gross errors in the measurements of x photoccordinates
can be detected and located, from the 2nd model on.
The functional mathematical model used are the collinearity
equations:
m11 (X-Xo) + m12 (Y-Yo) + m13 (Z-Zo)
x=f m31 (X-Xo) « m32 (Y-Yo) + m33 (Z-Zo)
(2.3.1)
sif m21 (X-Xo) + m22 (Y-Yo) + m23 (Z-Z0)
yeí 3i x-Xo) « mi? (Y-YO) + m33 (2-20)
Where mij are elements of the orthogonal matrix for spatial
rotations; x, y are photocoordinates; X, Y, Z are object space
coordinates; Xo, Yo, Zo are object space coordinates of the envolved
perspective center and f is the camera constant. This model applied
to photocoordinates of the fixed frame (say, left photo) is function
of Xi, Yi, Zi only, once the exterior orientation parameters are
hold fix. When applied to photocoordinates of the right photo, it is
function of wa, $2, k2, Xo2, Yo2, Z02 and Xi, Yi, Zi. Constraining
the previous and the new estimate object space coordinates, for the
points commom to two models, to be igual [11].
XP^ oR
x 1
XU 24 (2.3.2)
1 i
TOES
L 1
will allow the algorithm to detect gross errors in. the x
photocoordinates, at the same time that introduces the scale from
the second model on. (for the first, it is arbitrarely established).
Tables 2.3.1 - 2.3.4 show results of the application of the
algorithm.
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