The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part BI. Beijing 2008
21
3.1 Self-Calibration Method
Self-calibration is defined as the functional extension of the
Collinearity equations. Different two-dimensional additional
parameter (AP) models (physical, geometrical, or combinations
of both) are used for expressing the unaccounted systematic
distortions. However, there are certain problems with the self
calibration method:
■ Treatment of additional parameters as block or photo
invariants or combinations of both
■ Operational problems; that is, the total strategy of
assessing blunders, errors in control points, and systematic
errors
■ The determinability checking of APs; that is, excluding
indeterminable APs from the system
■ Significance testing of APs.
Each one of the above issues requires careful evaluation and
proper use of the APs. The successful solution of the normal
equations of the self-calibrating bundle adjustment is governed
by the extent of the correlation between the unknown
parameters (AP coefficients, exterior orientation (EO)
parameters, and object coordinates). If any two parameters, for
instance, are highly correlated, both tend to perform the same
function. In such a case, one or the other can be suppressed
without losing much information. Therefore, it is very
important to study the correlation structure of unknown
parameters and to check the determinability of APs.
Self-calibration APs compensate for the remaining distortion in
both object space and image space of a single camera. The
DMC has 4 physical PAN sensors; therefore, only a 4-quadrant
self-calibration of VIR imagery may become truly effective
(Kruck, 2006, Riesinger, 2006, Honkavaara, 2006, Jacobsen,
2007). However, the only purpose of such self-calibration is to
“unbend” the block during triangulation. For the sake of better
accuracy in object space, self-calibration may significantly
overcompensate the actual distortion in image space at the
frame edges. Also, it is very dependent on given object space
distortions. Therefore, under no circumstances should such
correction function be used in post-orientation math or applied
directly to VIR production. A reason for such
overcompensation is that the polynomial model has been
derived to effectively compensate systematic distortions in
areas concentrated around so-called Von Gruber centers or
similar arrangements in camera frame format.
This approach is useful when there is no precise GPS data and
no significant redundancy of image observations for sufficiently
dense grid computing is available. However, due to stiffness of
polynomial models, the resulting correction grid may have
significant overcompensation at the edges of the image frame,
which prevents the creation of a reliable ortho mosaic. When
self-calibration bundle adjustment is performed for the DMC,
the obtained EO can directly be used in the real-time math
models of almost any softcopy system without any extra on-the-
fly corrections, because the amount of image distortion itself
that directly propagates into the object space is much smaller
than the block bending caused by EO shift in Z. So, once good
EOs are obtained, the extra correction in image space is not
necessary. However, to ensure decorrelation of the obtained EO
from self-calibration parameters, a compensating single photo
resection on the densified triangulation (obtained in self
calibration bundle adjustment) is recommended. Once a self
calibrating bundle adjustment is performed, the obtained
triangulation is densified into control and the self-calibration
model itself is discarded. The following single photo resection
estimates the best EO that fits the image to the ground.
Unfortunately, not all photogrammetric organizations have
appropriate bundle adjustment programs and technical staffs to
perform such self-calibrating aerial triangulations. Furthermore,
some DMC users only deliver virtual images to their customers,
and they do not process or get into any photogrammetric
applications. Therefore, a better and simpler procedure is
needed to allow DMC owners to produce almost “distortion-
free” virtual images.
3.2 Correction Grid by Collocation Method
This method does not really belong to the camera calibration
methods mentioned above. In this method, some a posteriori
interpolation treatment is performed on the image residuals of a
bundle block adjustment. Calculated mean image residuals then
serve as correction values at the interpolation points of the grid.
The correction grid is able to remove the systematic errors in
the image plane that could not be computed or modelled by APs
in a self-calibration bundle adjustment. This correction grid
application works the same way as “Reseau” to refine image
coordinates for the local systematic errors by bi-linear
interpolation.
4. FLIGHT SPECIFICATIONS FOR CORRECTION
GRID CALIBRATION
In order to create a reliable correction grid array with
collocation techniques, a highly accurate ABGPS aerial
photography of about 200 to 400 images having 60% forward
overlap and 80% side overlap, with ground sample distance
(GSD) of 5-10, 10-20, 20-40 cm, and with a reasonable number
of well-distributed ground control points are required. At a
minimum, a single grid at 10cm may be computed.
A number of DMC blocks with different configurations are
used for this study. General specifications of some of these
blocks are given in Table 1.
DMC ID (Project Name)
DMC
50
DMC
48
DMC
27
Flying Height fm]
1000
800
750
GSD [cml
10
8
7.5
% Forward Overlap
80
80
60
% Side Overlap
80
80
80
Number of Strips/Cross
Strips
10/ 10
13/2
27/2
Number of Images
379
376
1105
Number of Control Points
8
21
39
Number of Check Points
6
20
14
Control Std Devs (X, Y,
Z) [cml
3,3,4
2, 2,2
3,3,3
GPS Std Devs (X, Y, Z)
[ cm ]
3,3,4
3,3,3
5,5,5
Table 1. Project specifications
The procedure to create the correction grid by Collocation
techniques is as follows:
