International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
Fig. 5: Camera EYESCAN M3 with glassfibre
illumination system
3. MATHEMATICAL MODEL
3.1 Basic model approach
The mapping of object points onto a cylindrical surface,
described by the rotation of the linear array sensor, complies
only in one image direction with the known central perspective
principle. Therefore, it was necessary to develop a geometric
model for the geometry of digital panoramic cameras. This
model is based on transformations between four coordinate
systems. As also described in (Lisowski & Wiedemann, 1998),
an object coordinate system, a Cartesian and a cylindrical
camera system as well as the pixel coordinate system were
defined. Through the transformation between these coordinate
systems we achieve the basic observation equations (equations
1 and 2) in analogy to the collinearity equations, which describe
the observations (image coordinates) as a function of object
coordinates, camera orientation and possibly additional
parameters.
"i t x
‘
Fig. 6: Geometrical model (Definition of used variables in
Schneider & Maas 2003b)
I VS
m= —-arctan + ZZ dm
x
A, 4
N (1)
N cz 1j,
nz c qpopopemu b rd"
2 AT £y
where:
xen =X) bas, (V1) +, (2-2)
yon, (XX), Q-X) n, (Z-Z) @)
zens QC X) (X) (2-2)
3.2 Additional parameters and accuracy potential
The geometric model complies only approximately with the
actual physical reality of the image forming process. Therefore
the correction terms dm and dn, where additional parameters for
the compensation of systematic effects are considered, are
crucial for the accuracy potential of the model. These
parameters are explained in more detail in Schneider & Maas
(2003b). The following figures (Fig. 7 and 8) illustrate three of
the additional parameters.
Rotation axis P
A
Fig. 7: Model deviations
(e,: eccentricity of projection centre)
Fig. 8: Model deviations
(v1, v2: Non-parallelism of CCD line, 2 components)
As a fist step. the geometrical model was implemented in a
spatial resection. The resulting standard deviation of unit
weight and other output parameters of the resection were
analysed to assess the effect of every additional parameter
individually. The following table (Tab. 2) shows how 0
changed by successively inserting additional parameters. The
spatial resection is based on approx. 360 reference points
around the camera position of a calibration room courtesy of
AICON 3D Systems GmbH.
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