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PERFORMANCE OF CIRCULAR IMAGE BLOCKS IN CLOSE-RANGE 
PHOTOGRAMMETRY 
Jussi Heikkinen 
Helsinki University of Technology 
Institute of Photogrammetry and Remote Sensing 
Finland 
Commission V, WG V/1 
KEYWORDS: Photogrammetry, Adjustment, Block, Estimation, Bundle, Close Range 
ABSTRACT 
In this paper the circular image block-method and its applicability is discussed. Circular image block approach is not meant to 
substitute the current close-range photogrammetric network desi gn methods, but simply to provide a new tool to be used with current 
methods in special measuring conditions. Feasibility in general and limitations of this method is discussed. The change of block 
parameters and its effect on object points is revealed with simulated tests. The restricting conditions and recommendations leading to 
successful block adjustments are presented in final conclusions. 
1. CIRCULAR IMAGE BLOCKS 
The circular image block-method is especially meant for 
measurements of fairly large objects. This approach is 
beneficial in special conditions where the traditional approach 
in network design problem meets its limitations. These kinds of 
cases appear when visibility is some how compromised, like 
with very complex object structures. The only solution to this 
problem is to take cameras inside the object space, which often 
leads to construct a set of smaller image subblocks. These 
subblocks then have to be transformed into common coordinate 
system afterwards. The reason why all image measurements are 
not handled in same adjustment is that usually the network 
geometry in such cases is too weak and common bundle 
adjustment would lead to deformations in object model. Rigid 
conformal transformation is usually used for transferring the 
submodels into common coordinate system. This kind of 
approach unfortunately generates quite a number of subblocks 
and some image management system is then required to manage 
the whole measuring project. Also, more effort has to be put in 
search of correspondent object features for coordinate 
transformation purpose. What makes these cases so difficult is 
that we have numerous subblocks to be handled in the same 
project and the orientation of subblocks can be quite arbitrary in 
object space. 
Circular image block-method will reduce the number of 
subblocks needed in photogrammetric measuring tasks, as well 
provide a better geometry in photogrammetric network. Image 
block design called here 'Circular Image Blocks' is a block of 
images who share common properties. All camera positions in a 
block have the same property that their projection centres lie on 
the same plane in object space. Another relation between 
projection centres is that a single circle on that plane can be 
drawn which goes through all the projection centres and 
orientation of camera is static respect to the trajectory of this 
circle. The final assumption is that successive images have 
overlap between them and overlap also exists between the first 
and last image in the block. 
These are quite strict assumptions, but thinking of imaging 
arrangements in practice, it is quite simple actually. By using a 
rod with certain length for the purpose, this can be done. The 
camera is fixed in one end of the rod and the other end will be 
fixed to some stationary point. The rotation of the rod is only 
enabled around this stationary point on a specific plane. This 
will fulfil all the previously mentioned requirements for the 
image block. This yields to an image block covering the scenery 
of full 360? deg from one point. The image measurements will 
be the correspondent image points on successive images. The 
weakness of such block is that all successive camera positions 
have divergent orientations. In order to overcome this problem 
two co-centric image blocks are recommended to be constructed 
and adjustment of both blocks should be done simultaneously. 
This adjustment should also include estimation of angular 
difference between these two blocks. The difference between 
two blocks is that in the first block the camera is fixed to the rod 
in perpendicular direction, and in the other block camera is 
turned into opposite direction. So from two blocks we can find 
camera positions with converging viewing directions at most 
two times the length of the rod apart from each other. 
2. MATHEMATICAL FORMULATION 
The whole idea is that we can bind multiple images into two 
image blocks and substitute their orientation parameter with 
fewer block parameters. Cause we are handling a constrained 
image block we might introduce few constrain equations into 
adjustment process. In here we just reparametrize the image 
parameters in the image block in order to fulfil the requirements 
for the block. We have here a freenet type estimation problem. 
We don't have any known co-ordinate information, instead we 
create a co-ordinate system of our own. In order to fix the 
datum we might minimize the sum of variancecovariances of 
the parameters, which is a common approach to solve 
insufficient datum problem. Another approach, which we have 
used, is to fix sufficient number of parameters in order to 
overcome datum defect. We have fixed few parameters and 
formulated new type of formulations, which describe the 
imaging condition in our block. The rotation of the camera in 
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