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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BYF. Istanbul 2004
Mi Hs UP
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A system of kind (2) could be composed for each measured
image point i. This means that if the object is photographed by
one stereopair, each point from the object would originate two
systems of kind (2) or in total 4 equations, since each point is
appeared on two photographs.
1.4. Unknown quantities
In case that the survey is performed by a metric camera, each
bundle (photograph) contains 6 unknowns: the tree rotation
angles «y $ and «, defining the matrix AR, and coordinates (X,,
Yo, Zo) of the projection centre O. Since each measured image
point originates 2 equations, in order to define synonymously
one bundle, 3 control points are sufficient. Also 3 points are
sufficient for calculation of one stereopair, as long as the points
are located in the overlapping area of the photographs.
In case that a nonmetric camera is used, the elements of
internal orientation x,, yo and f are not defined, which means
that the unknowns for each bundle get increased with 3. In order
to secure a synonymous solution for the 9 equations, 5 control
points are needed. Since the number of equations usually is
larger than the minimum required and the measured image co
ordinates contain casual errors, the least squares adjustment is
applied.
1.5. Additional parameters
Lens distortion, as well as some other possible defects of the
camera, are origin for systematic errors in image coordinates,
because the images get drawn away from correct central
projection. One of the conditions of the least squares adjustment
is that the adjusted quantities should not contain systematic
errors. With amateur cameras, as distinct to professional
cameras, these defects may have significant values and hence
may considerably disturb the processing.
If the lens distortion is known, the image coordinates may be
adjusted before the bundle adjustment. This process is know as
image refining. Even in case of some distortion, the refining is
ineffective, because with nonmetric cameras it gets changed in
time. It is more effective for the image defects to be reduced by
introduction of additional parameters into the mathematical
instrument:
m (X, = X,)+m,(Y, = Y) +m, (2, = Zu)
 X,)* m, tr, Y,)«m,(Z, 23
(4)
my, (X, = X,)* m, (y, = Y), + My; (Z, = Zi}
Yep, tA =f
v=o + dy, == :
me t f m, (X, = X,)* m, 17 SE y, )+ m,,(Z, 7 20)
where the additional parameters Ax, and Ay, are function of
some unknowns and take part in adjustment together with the
rest of unknowns.
The selection of additional parameters is based on two
contradictory principles:
e The number of parameters should be as less as possible, in
order to reduce the number of control points, and
respectively to reduce the volume of calculations.
137
e. The number of parameters should be as large as necessary
to ensure minimum corelation with the other unknowns.
Otherwise it is possible for the normal matrix to get
degenerated.

In contrast to the traditional photogrammetry, where the
additional parameters may be considered as constants for all
photographs within a block or at least for a group of
photographs, the use of nonmetric cameras may require a full
set of additional parameters for each single photograph. This
leads to an increase of the amount of calculations, which
however is not a serious problem, because the blocks made by
nonmetric cameras usually are smal.
2. EXPERIMENT
An experiment has been conducted, aiming to determine what
accuracy may be reached at closerange photogrammetry when
nonmetric digital camera with unknown elements of internal
orientation and distortion of lens is in use.
2.1. Surveying
The frontage of a residential building, located in City of Sofia,
has been surveyed by a total station Leica TC 1610
geodetically. By means of intersections 55 not marked survey
points have been defined. The error of their location is within
the range of +0.5 cm.
The same frontage have been surveyed photogrammetrically
with one stereopair. The distance beteen the camera and the
object is about 20 m, while the distance between the two
projection centres is about 4 m. The main camera optical rays
+ 23m +
=n ç


B, 20m
JB 9—9o A 
1 4m 
so 5. y
++ 4m
B,B»  geodetic basis
S, S2  projection centre
Figure 1. Survey performance
are approximately parallel and inclining towards the vertical
plane. The pictures has been taken by means of an amateur
digital nonmetric camera Canon S230 with a focal lenght,
corresponding approximately to 35 mm and size of 3 mega
pixels of the photographs.
2.2. Processing
The images have been processed by PHOTOMOD Lite — a
photogrammetric software of Racurs Co., allowing operations
with nonmetric cameras. The calibration with this software is
done during the processing. The lens distortion can be taken
into consideration only in case that it has been defined before
hand.
For the purposes of this experiment, the orientation of the
stereomodel has been conducted by means of 8 control points
and 30 tie points. The lens distorsion is unknown. For the sake
of reduction of distortion influence, the edge zones of the