PInned Target Array
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Camera Stations
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Targets
Figure 1. network geometry, detailing target array, all
camera stations and survey simulation targets.
2.2 High precision estimation of reference target
coordinates
One ofthe main requirements for the computation of target
coordinates was for a datum which would not introduce
shape distortions into the object space. Such a datum could
be defined by the method of inner constraints, in which the
seven elements of datum definition are defined by the
target coordinate starting values.
The target array was photographed on two occasions, with
a variety of cameras including a UMK 10/1318, a P32, a
reseau equipped Hasselblad SWC with a variety of film
and camera back combinations, and also an unmodified
Hasselblad SMC. Photographs on glass plates as well as
film were made with all cameras.
All target images were measured three times using the
NPL ZKM measuring microscope. For each frame the
target array and reseau images were automatically driven
around with manual setting of the measuring mark on each
point. The comparator coordinates produced could then be
processed according to the reference mark system
available in each camera.
Some of the results of these experiments have been
discussed in Robson 1990 and 1991a. This paper will
concentrate on data sets from two of the cameras; the
UMK 10/1318 using Agfa Holotest 10E75 glass plates
(Agfa 1989, Cooper and Robson 1990); and on images
from a modified Hasselblad SWC used in conjunction
with a 120 film back and Kodak Technical Pan film
(Kodak 1987).
The main free adjustment incorporated a network with 9
physical cameras, 60 images and 3654 target image
measurements. Results from the adjustment pertinent to
this discussion are described in table 1. The variance factor
associated with this adjustment is significantly greater
than unity primarily because the image measurements
were considered as independent stochastic variables. The
photo-coordinates from each frame must be physically
correlated, not least because film unflatness is asystematic
effect. Correlation between measurements is difficult to
determine in practice and generally requires that the
variance components be estimated as unknowns in the
adjustment (Kilpela 1980, Torlegard 1989). Such a
variance component analysis is not pertinent here because
the twin photo networks with which we are concerned
cannot support such an estimation due to high internal
correlation.
The cameras used did not conform to the assumed
colinearity model, so additional parameters were included
to model focal length, departures of the principal point
from the optical axis and lens parameters to model radial
and tangential lens distortions (Fryer 1988). These were
estimated in the main free adjustment, one set of
parameters for each physical camera. The resultant
parameter values could then be used as starting values in
subsequent adjustments each parameter being constrained
by its standard error. In this way best estimates of the
physical properties of each camera lens cone could be
included. Since film deformation could also be partially
modelled by these parameters, all reseau images in the
main adjustment were corrected for film deformation.
Correction was carried out using the local bilinear
correction, since this too provided a best estimate of the
actual deformations occurring, independent from the
bundle adjustment.
Table 1. Some parameters from the “free bundle
adjustment" incorporating all images
Degrees variance RMS RMS object space
of Factor photo-coordinate| coordinate standard
Freedom residuals deviations
6702 | 1.290 x: 2.58 um X: 57 uum
y: 3.07 um Y: 45 um
Z: 45 um
2.3. Adjustments based on simulated survey control.
To investigate effects of image deformation on the object
Space a survey was simulated. Some of the target
coordinates estimated from the free adjustment were
constrained by standard errors of Imm, a value considered
reasonably obtainable from a three station theodolite
control survey. Two target configurations were used, the
first covering the whole test field area (11, 15, 52, 81 and
95) and the second with reduced control at the top right
corner (11, 23, 52, 81 and 95) (Figure 1).
À set of adjustments was carried out using both the UMK
and modified Hasselblad photo-coordinate data sets. In
both cases each adjustment permutation was run with the
appropriate complete set of photographs and then using
the top left and right images as a convergent pair.
The reseau present in the modified Hasselblad camera
permitted the application of several different film
deformation corrections (Ziemann 1980):
(i) Raw plate; simply the comparator coordinates
transformed to the photo coordinate system by treating the
four corner reseau marks as fiducial marks. No calibration
of the fiducial coordinates was assumed, the approach
simply used least squares to fit a square axis through the
coordinates. This approach is analogous to that applied to
the UMK images.
