1. The Influence of the distribution of ground
control points on the accuracy of the
aerotriangulation calculation
RNDr. Jakub Miřijovský
This presentation is co-financed by the
European Social Fund and the state
budget of the Czech Republic

2. Introduction
Control points are the most essential elements for the correct
processing of aerial photographs.
Control points serve as a basis for the calculation of exterior orientation
parameters.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

3. Distribution
The distribution of control points is decisive for the AAT result and its
accuracy.
Normally 4 or 5 symmetrically distributed points are used in practical
conventional aerial photography (Pavelka, 2003)
A question is: what does "symmetrical" mean?
The points should be evenly distributed over the entire area of the
photograph.
There are many ways how to distribute the points.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

4. Mathematical background
The error rate of the model increases if there is a linear relation
between the points.
The addition of equations for the third point, which is located on a line
connecting two other points, will not increase the rank of the matrix.
An Example:
Six unknowns = Six equations
Two points will produce four equations (two for X and two for Y)
If we add a third point, which, represents a linear combination of
the two preceding points, then even the other pair is still a linear
combination of the previous points.
The resulting system then brings nothing new and the entire system
cannot be solved
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

5. From the theory to the reality
The maximum accuracy can be reached if none of the three points lie on
a line.
It is difficult to achieve in the terrain.
Natural and artificial obstacles present a serious limitation.
More complicated in UAV photogrammetry
A large value of a radial distortion.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

6. From the reality to the expereiment
An experiment conducted in laboratory conditions tries to prove or
disprove the effect of distribution of control points on the accuracy of
determining the exteriror orientation parameters.
Progress of the experiment:
A sheet of graph paper was placed on a plane surface.
The planeness was achieved by application of an accurate digital
level.
The values of the GCP in the Z coordinate was zero.
The paper was fixed to a balanced board with adhesive tape.
The camera was put on a tripod. The image field covered the
entire surface of the photograph.
The height of the camera was measured with a ruler.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

7. From the reality to the expereiment
Course of the experiment:
The camera was also levelled, thus producing an almost exactly
vertical axis for the photography.
The centre of the image was marked on the graph paper with
regard to the focusing point in the viewfinder.
An image was taken.
The camera with the tripod was moved and another photograph
was taken under identical conditions with the previous photo.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

8. From the reality to the expereiment
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

9. From the reality to the expereiment
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

10. Image processing
Three model situations for distribution of control points were measured
on the graph paper by a calibrated ruler in an interval of one
centimetre.
The total number of control points was fixed for all the situations and
was specified as fifteen.
The points' coordinates were read from the graph paper after
measurement with a calibrated ruler.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

11. Image processing
1. A completely wrong situation, when the points are not evenly
distributed and all lie in a single line and along one side of the
imaginary terrain. This situation can occur in UAV photogrammetry
when a watercourse is photographed and the points cannot be
distributed along the other side of the watercourse.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

12. Image processing
2. Applicable distributions where the control points are distributed evenly
over the photograph, but individual groups of points have a linear
relation. Theoretically, this distribution should give a usable solution.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

13. Image processing
3. Ideal distribution of points over the image. None of the fifteen control
points lie on the same line; the software must use a maximum number
of triangles for a correct calculation. In theory, this version should offer
the best solution.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

14. Image processing
All the versions were processed with an identical adjustment.
The overall calculation is also affected by other errors besides the mere
position of the points.
One of the most significant is an accurate determination of the actual
coordinates.
For the experiment, they were regarded as accurate and constant for
all the versions.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

15. Results
The results are in the statistic reports.
Variance of determining of each coordinate was used for the evaulation
of AAT.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

16. Results
The height of the photographing = 38 cm
The height of the photographing = 100 m, the error = more than 1 m.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

17. Conclusion
The effect of correct distribution of control points in the terrain on a
correct calculation of the external orientation objects is not negligible.
As expected, a version in which all the points are located in a single
line, thus having a linear relation, has proven completely unsuitable.
Distribution of points along a straight communication or other objects
in the terrain is by no means recommended.
If it is at all possible, it is always best to keep the rule of an even
distribution of the points over the surface so that none of the points
lies on the same line with another point.
This version in fact corresponds to an absolutely random distribution of
the points.
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

18. Thank you for your attention
jakub.mirijovsky@upol.cz
First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc