This presentation is co-financed by the

European Social Fund and the state

budget of the Czech Republic

The Influence of the distribution of ground

control points on the accuracy of the

aerotriangulation calculation

RNDr. Jakub Miřijovský

First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

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

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

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

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

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

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

From the reality to the expereiment

First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

From the reality to the expereiment

First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc

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

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

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

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

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

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

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

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

Thank you for your attention

jakub.mirijovsky@upol.cz