supposed to be done on xz-plane. So all camera poses have their 
y-coordinate fixed to zero. Also the x-axis is fixed into direction 
of the first camera pose of the first image block and origin of 
the co-ordinate system is in centre of rotation. All other camera 
pose co-ordinates are expressed in polar-co-ordinates. 
x=rcosa, 
z=rsind, 
(1) 
The rotation of the camera in each camera pose respect to this 
local co-ordinate system is also dependent of this one parameter 
a, unique for each camera pose. Also it is dependent of the 
orientation of first camera pose in image block. 
Rz Ros, 
D,P,K 
(2) 
Here rotation matrices R are assumed to be 3x3 orthonormal 
rotation matrices, where rotations are supposed to be done 
subsequently. So for each image block we have four common 
parameters ,,k and r and for each camera pose we only have 
one unique parameter a. Only for first camera pose of the first 
image block we have fixed the a=0. This way we can express 
the block with fewer parameters in more compact forms and get 
benefit of overdetermination in our measurements. This way we 
can construct the image block but by adding at least one 
distance measurement we can also have our image block in right 
scale. 
3. ACCOMPLISHED TESTS 
The performance of a circular image blocks can be tuned by 
changing few factors in construction of a block. One is the 
length of the used rod. In principle, longer the rod, better the 
precision. The length of the rod plays here the same role as the 
base length in stereoscopy. However, in practice the imaging 
environment can limit the length of the rod. The space where 
camera is supposed to be rotated is tight or extending the length 
also changes the view and objects closer to the center will be 
out of sight. To illustrate the effect of length of the radius, tests 
were accomplished with simulated data. Fictitious circular 
image blocks with differing radii were constructed in center of a 
randomly generated object point set. Simulated image 
observations were obtained by backprojecting the object points 
on images according to block geometry. Simulated random 
noise on some level was added to observations and adjustment 
of a block was performed. The result of the simulation shows 
that the effect is not totally linear and after some limit, the 
extension of the radius does not improve the result significantly. 
This is without question also dependent of the structure of 
object point set. Further the object point locates more 
significant is the improvement of point precision. The standard 
deviations of co-ordinate values respect to distance are depicted 
in Figure 1. The standard deviations are calculated from 100 
simulated test runs with normal distributed noise added at level 
of 0.2 pixels. The polynomial curve is fitted into data, where the 
mean co-ordinate standard deviation is depicted on ordinata and 
the distance of 3D point on abscissa. A curve is fitted into all 
data sets of different radii. The camera geometry is chosen to be 
1024 x 1280 pixels with 1400 pixels camera constant. The 
camera model resembles the geometry of the camera used in 
real examples. 
  
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Figure 1 Change in co-ordinate standard deviations relative to 
distance. Each curve depicts one length of radius. 
The same procedure was followed while testing the noise level 
of the image measurements. This test simulated the use of 
different quality imaging instruments. Similar type of 
presentation can be seen in Figure 2. 
  
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Figure 2 Change in co-ordinate standard deviations relative to 
distance. Each curve depicts values with different noise level. 
The chosen noise levels are 0.5, 0.2, 0.05 and 0.02 pixels. The 
first two cases can be considered to be as bad and good image 
measurements of natural object points and the latter two as bad 
and good observations of targeted object points. The camera 
model is the same as with the previous test. The noise levels can 
also be thought as different quality or resolution of imaging 
device. 
The change of number of images in a block was also tested in a 
similar way. Normally it can be stated that increasing the 
number of images does not improve the precision much, unless 
the whole imaging geometry of the photogrammetric network is 
improved. This holds in traditional networks where each new 
camera position brings six new parameters in estimation. In the 
approach presented here, one new camera position adds only a 
single parameter in adjustment and redundancy is essential. This 
is due to use of polar coordinates for presenting the projection 
centers in formulation of mathematical model of circular image 
block. From Figure 3 we can see that increasing the number of 
images and observations improves the precision upto 100 
frames per block, but after that no significant improvement can 
be seen. 
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