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# Miřijovský, J: The Influence of the Distribution and Amount of Ground Control Points on the Accuracy of the Aerotriangulation Calculation

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### Miřijovský, J: The Influence of the Distribution and Amount of Ground Control Points on the Accuracy of the Aerotriangulation Calculation

1. 1. The Influence of the distribution of ground control points on the accuracy of the aerotriangulation calculation RNDr. Jakub MiřijovskýThis presentation is co-financed by theEuropean Social Fund and the statebudget of the Czech Republic
2. 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. 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. 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. 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. 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. 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. 8. From the reality to the expereiment First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
9. 9. From the reality to the expereiment First InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc
10. 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. 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. 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. 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. 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. 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. 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. 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. 18. Thank you for your attention jakub.mirijovsky@upol.czFirst InDOG Doctoral Conference, 29th October - 1st November 2012, Olomouc