ACCURACY ANALYSIS OF CIRCULAR IMAGE BLOCK ADJUSTMENT
Jussi Heikkinen
Institute of Photogrammetry and Remote Sensing
Helsinki University of Technology, P.O.Box 1200, FIN-02015 Espoo, Finland
Jussi.Heikkinen @hut.fi
Commission V, WG V/1
KEY WORDS: Photogrammetry, Adjustment, Bundle, Block, Estimation, Close Range
ABSTRACT:
Circular image block method has been developed for special photogrammetric close-range cases. Circular image block
approach is not meant to substitute the current close-range photogrammetric network design methods, but simply to
provide a new tool to be used with current methods. This method is beneficial in conditions where the traditional approach
in network design problem meets its limitations; in cases when the photogrammetric network and camera stations cannot
be around the object, but the imaging has to be done inside the object space. A new mathematical model had to be
designed for the spherical imaging. However, this method is based on block of individual bundles of rays unlike the
panoramic imaging. In this paper the method in real measuring tasks is evaluated in terms of accuracy and robustness.
In order to evaluate the performance, a practical test was accomplished by measuring an object point set with varying
object distances. Results are compared with reference data as well as with results of the simulated tests with similar
test parameters. Discussion is given about the problem of initial values and the suitability of the method in an object
reconstruction project.
1 INTRODUCTION
The circular image block method is especially designed
for measurements of fairly large objects and for special
photogrammetric close-range cases. This approach is ben-
eficial in special conditions where the traditional approach
in network design (Fraser, 1989) problem meets its limi-
tations; e.g. when visibility is some how compromised
like with very complex object structures. The only sol-
ution to this problem is that imaging has to be done in-
side the object space, not around the object. This often
leads to construct a set of smaller image sub blocks, which
have to be transformed into a common coordinate system
afterwards. The reason why all image measurements are
not handled in same adjustment is that usually the net-
work 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 sub models into common coordinate sys-
tem. Unfortunately, this kind of approach generates quite a
number of sub blocks and some image management system
is then required to manage the whole measuring project.
Also, more effort has to be put in search of correspon-
dent object features for coordinate transformation purpose.
These numerous sub blocks are difficult to handle in the
same project and their orientation can be quite arbitrary in
object space.
Circular image block method will reduce the number of
sub blocks needed in photogrammetric measuring tasks, as
well provide a better geometry in photogrammetric net-
work. Image block design called here "Circular Image
Blocks’ is a block of images who share common proper-
ties. All camera positions in a block have the same prop-
erly 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 cam-
era 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 im-
age in the block.
These are quite strict assumptions, but in practice, it is
quite simple actually to fulfill the conditions by using a rod
with certain length for the purpose. 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 around
this stationary point on a specific plane. This yields to an
image block covering the scenery of full 360° deg from
one point. The image measurements will be the correspon-
dent image points on successive images. The weakness
of such block is that all successive camera positions have
divergent orientations. In order to overcome this prob-
lem two co-centric image blocks are recommended to be
constructed and adjustment of both blocks should be done
simultaneously including estimation of angular difference
between the blocks. The camera is fixed perpendicularly
to the rod. In the first block in direction of +90° and in the
second block —90°. This way we can find camera posi-
tions with converging viewing directions at most two times
the length of the rod apart from each other, see Figure 1.
The whole idea is that we can bind multiple images, bun-
dles of rays, into two image blocks and substitute their
orientation parameter with fewer block parameters. As
we are handling a constrained image block we might in-
troduce few constrain equations into adjustment process.
Our approach is to reparametrize the image parameters in
the image block in order to fulfill the requirements for the
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