Praca Dyplomowa - Photogrammetry and Remote Sensing - AGH

THEORETICAL BACKGROUND
The bundle adjustment has a lot of advantages, because it may be applied with irregularly
arranged and often unfavourable image configurations. It is more complex structure of normal
system of equations. There is complex generation of approximate values for the unknowns
and arbitrary oriented object coordinate systems. It is possible to combine adjustment of
survey observations and conditions, where also several imaging systems can be calibrated
simultaneously.
Adjustment model - Gauss-Markov linear model - based on collinearity equations
This principle is based on that the unknown parameters are estimated with maximum
probability.
Condition for the residuals results (L2 - normalization):
∑ [ ]
Mathematical model of the bundle block adjustment is based on the collinearity equations,
which are mentioned before in equation (2.8) above.
18
(2.10)
The structure of these equations allows the direct formulation of primary observed values
(image coordinates) as functions of all unknowns‟ parameters in the photogrammetric
imaging process. The collinearity equations, linearized at approximate values, can therefore
be used directly as observation equations for least-square adjustment according to the Gauss-
Markov model.
It is principle of the image coordinates of homologous points which are used as observations.
The following unknowns are iteratively determined as functions of these observations.
� 3D object coordinates for each new point i (up, 3 unknowns each)
� exterior orientation of each image (uI, 6 unknowns)
� Interior orientation of each camera k (uc, 0 or ≥ 3 unknowns each)
The bundle adjustment therefore represents an extended form of the space resection:
Where:
i – point index
j – image index
k – camera index
(
(
Standard form, the linearized model (functional model):
With n observations and u unknowns, n>u.
⏟̂
⏟
⏟
̂⏟
)
)
(2.11)
(2.12)