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Densification of trigonometric nets — practical experiences with bundle adjustment
Photogrammetria, 35 (1979) 29--36 © Elsevier Sci.entific Publishing Company, Amsterdam -- Printed in The Netherlands
29
D E N S I F I C A T I O N O F T R I G O N O M E T R I C NETS - - P R A C T I C A L E X P E R I E N C E S WITH B U N D L E A D J U S T M E N T
JONNA HVIDEGAARD CaHunavej 19, 3450 Alleroed (Denmark) (Received May 10, 1977; revised and accepted January 13, 1978)
ABSTRACT Hvidegaard, J., 1979. Densification of trigonometric nets -- Practical experiences with bundle adjustment. Photogrammetria, 35: 29--36. Fixed-points for cadastral measurements have been coordinated by use of the bundleadjustment method. The coordination was done by densification of an existing 2-kin vet of triangulated points down to a density of approx. 400 m. The photo scale was 1:t~000--1:10000 and the overlap 60/30. The accuracy of 11 blocks, covering an area of 631 km 2, has been tested in the field by measuring distances between coordinated points. Approx. 850 points were checked and ~ave a standard error of 5 cm on a photogrammetric coordinated point.
BACKGROUND
P h o t o g r a m m e t r y has already been used for some years for cadastral purposes in Denmark. To a certain degree, p h o t o g r a m m e t r i c plans have folml~d the basis of n e w cadastral maps. Perhaps more interesting in this c o n n e c t i o n is the fact t h a t p h o t o g r a m m e t r i c a l l y coordinated fixed-points are being used for cadastral measurements. The Geodetic Institute of D e n m a r k is responsible for t h e triangulation of higher order. The institute establishes points d o w n to a density of approx. 2 km. Further densification is left to t h e Cadastral Service and private surveyors. According to official regulations, t h e surveyors have to tie n e w cadastral m e a s u r e m e n t s to fixed-points w h e n these are located w i t h i n a distance of 200 m (for measuring roads the limit is 500 m). This means in practice t h a t unless one has a n e t of p o i n t s with a d e n s i t y of approx. 400 m, pr.~blems m a y arise especially in t h e developing areas of larger towns. Also, local authorities have a professional interest in t h e develoj~ing areas of the towns. One of t h e m a i n jobs for t h e p h o t o g r a m m e t r i c f i n n s is to p r o d u c e technical plans o n t h e scale 1 : 1 0 0 0 for the municipalities. The need for ground control for t h e compilation o f these plans corresponds very well w i t h t h e earlier m e n t i o n e d 400 rn net. T h e n e t is f u r t h e r m o r e useful for the local technical a d m i n i s t r a t i o n for m a p revision and setting o u t p~lrposes.
30
The jobs that will be presented in this paper are all the result of cooperation between a state authority, namely the Cadastral Service, a private photogrammetric firm, the local municipality: and the local private surveyor. THE PHOTOGRAMMETRIC
TRIANGULATION
Up to 1970 the only photogrammetric triangulation method used for the kind of jobs described was the Anblock, with models measured in analogue instruments such as A8, A7 and Simplex III. This method is still in use for smaller blocks and gives sufficiently good results with a photo scale of 1:4000 or 1: 5000. In 1970 the first test block in Denmark using bundle adjustment was made. The measuring and the calculations were done in Finland at the Technical Uniw~rsity of Helsinki. The results were promising, and since then some 50 jobs covering approx. 2000 km 2 have been performed, mainly in Finland but lately also in Denmark. All the jobs mentioned in this report were carried out in Finland. The pictures were measured on a Zeiss PSK comparator using glaswdiapositives and the calculations were made with the Finnish triangulation programme. Prior to the adjustment the pictures were corrected for: (1) film distortion (using affin transformation on the fiducial marks), (2) lens distortion (radial), (3) refraction, and (4 } earth curvature. Cr:iteria had to be established for the practical execution. When we started only very little had been published about practical results of point densification by aerial triangulation, and bundle adjustment was not yet very widely used. An early report was given by G.C. Tewinkel (U.S.A.) at the commission III symposium in London 1971 (Tewinkel, 1971). Since then a lot of things have been happening in that field. The development in the U.S.A. is described by W.V. Hull (1975), and in Germany e.g. tests using the Anblock method on models computed from comparator-measurements have been carried out in Stuttgart (Ackermann, 1976) and reports on bundle adjustment axe given by H. Bauer (1974) from Hannover. But 1970 was still ~airly early in this connection so we had to set our standards mainly on the basis of theoretical investigations (Malinen, 1969; Kilpel~i, 1970 ). The intention was to end up with a standard point error (x/n,2x + r~y ) of 5 cm on the ground, and after many considerations the following l~nes of direction were proposed: (1) Photo scale between 1:8000 and 1:10000. The predicted accuracies of the bundle-adjustment were 4--6 ~m in photo scale. (2) The cameras had to be the ordinary wide-angle cameras of the photogrammetric firms (c - 15 cm) and the film the normally used black and white panchromatic.
31
(3) Overlap q50/30 was chosen. Certainly, 60/60 would form a stronger block (Malinen, 1969; Tewinkel, 1971), but as the improvement is mainly on the Z-coordinate, and considering the increase in number of photographs in a block, 60/30 was agreed upon. In some cases 80% forward overlap was photographed. Not all the pictures were used in the block, but selections were done in order to "get d o w n " into streets, to get pictures in a good position in one strip compared to the next strip, or to fortify the block in weak areas by including extra pictures. (4) The distribution of ground control points was chosen according to the following scheme: Planimetric control along the perimeter of the block with a mutual distance of 4 X base. Height control as a net covering the whole block, the density being 2 X base. These figures are recommended by Dr. Kilpel~i from the Technical University of Finland in his investigation using simulated bloc~;s (Kilpel~i, 1970). Remembering the 2-kin net of triangulated points already existing in Denmark, the figures outlined the prospect of never having to measure anything but vertical control points in the field. These expectations have only been fulfilled to a certain extent. In a block it will normally be necessary to measure horizontal control points in 2--3 positions. The vertical controls all have to be measured and in spite of the fact th,~t the Z-coordinate is only of minor interest, at least from a cadastral point of view~ ~t was agreed to use the recommended net. (5) The accuracy of the triangulated points was stated by the Geodetic Institute in the following way: The maximum error on a distance between two n,~ighbouring points is 10 cm. As to the accuracy of the vertical control points the stavdard error was predicted to be 2--3 cm. (6) For targets white plates of 40 X 40 cm were chosen and a black contrast o~Yat least 15 cm around the signal was recommended. All ground control points should have extra signals (Fig. 1) first of all to ensure the identification in the pictures. (7) Artificial points (marked in the emulsion) were abandoned mainly because of unfavorable experiences from Anblock jobs. Where extra passpoints measured d i s t a n c e s
extra signal
control point
extra signal
measured d i s t a n c e
Vq control point Fig. 1
direction to knovn point
extra signal
32
were needed, either signals were set out in advance in the predicted side-lap and perimeter, or natural points were measured in the comparator. Broadly speaking these lines have been followed in the reported jobs. TEST Having made a number of blocks with the new method it seemed natural to check whether the results were in accordance with the expectations. Also, the possibilityof reaching the goal of 5 c m in standard error had been questioned. In order to certify an accuracy of 5 cm, a very exact geodetic measurement is required. At the same time the test should be fairly easy to carry out since a secondary aim of the investigation was to see whether a test could be done in a way that would make it reasonable to include it as a permanent part of future densification jobs. As the standard error of a distance can be shown to be equal to the standard error of a point, under the assumption of independence between the coordinates, measurement of distances would give the wanted result directly. Furthermore, the very simple geodetic " n e t " would give no error-propagation, and by using electronic distmlce-measuring equipment (EDM) the measurements could be of high accuracy. The standard error one gets by using distances is the relative one, but this is also the error of major interest here, as the coordinated points are going to be used for cada~tral measurements in the classical way. Having decided to use distances, the next problem was how to plan the field work. To allow the use of the normal distribution, the elements (these being the differences between the measured distance and the same distance calculated from the photogrammetric coordinates) must be independent. If one uses EDM the easiest way to g~t many controls would be to measure several distances from the same station, but then the elements are not independent. However, measuring only one distance from each point would increase the control work and the costs considerably. The actual work was done as a compromise between these two extremes, and calculations afterwards showed that *.he correlation was hardly ever significant. In all the jobs but one, the measured distances have been regarded as error-free. This is of course a point where one has to be careful. In the start of the collection of controls we also intended to use distances measured by the local su~leyors during their normal work. It appeared later that the standard error here (based on the remeasurement of 118 distances) was approx. 5 cm, which is the same as the expected error to be controlled. Out of 40 double measurements (never from the same station) the standard error on a distance measured by the testing group is computed to be just under 1 era.
33
0 C~
c~
C) 0 ,°
,°
o,
°°
°°
°°
°.
°°
°°
°°
°°
s~ "7'
I
I
II
I
c~
C)
pm~
C~
.=.
im=l
r.T.l
34
, ° , . ° °
O
O
O
~
. , °
O
O O O O ~ O
~
O
O
~
~
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O
~00
O
O
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N
NN
~
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O
~-~ ÷ ÷
~ +
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~.
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,
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~ ÷ ÷ +
÷÷
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4-"
O
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,~,<
,<
<
~<
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<
35
It has to be m e n t i o n e d t h a t quite a few of the distances were in fact measured w i t h steel-tape, b u t as it appears from Table II t h e y were all u n d e r 10 m. These short dista:lces date f r o m double-signalized points where b o t h t h e point itself and t h e extra signal have b e e n coordinated. RESULTS The results are presented in Tables I and II, the firstone dealing with the actual flight mission and the calculations, the second with the control measurement. As can be seen from Table I, the side-lap and the photo scale vary to some extent. When a c o n t r a c t is set up for a flight program, a variation of + 10% is usually allowed in t h e side-lap. Nevertheless, some of the blocks on the list seem to have been p h o t o g r a p h e d in rough weather. As to the p h o t o scale it has to be m e n t i o n e d t h a t right f r o m the start one of the p h o t o g r a m m e t r i c firms wanted to use 1:8000 instead of 1:10000. The same firm uses 1 : 4 0 0 0 for low flying w h e r e t h e others prefer 1:5000. Therefore, t h e figures in the table should n o t solely be e x p o u n d e d as a growing confidence in the m e t h o d . T h e table does n o t tell a n y t h i n g a b o u t t h e distribution of t h e ground control points. An investigation showed t h a t c o m p a r e d with the r e c o m m e n d e d distribution, there were m o r e horizontal controls (mainly points inside the block) b u t less vertical controls (the net being closer to 3 × base t h a n to 2 × base). In Table II it has to be noticed t h a t t h e standard error of one of the tests TABLE III Block
Adjustment
Contro~ RMS (cm)
oo
(ca) .
Arhus 1971 Alborg 1971 Jersie 1971 Arhus 1972 Alborg 1972 Ellidsh~j Arhus 1973 Alborg 1973 Ajstrup HCje T~strup 1973 Alborg 1973 N~$rholm Alborg 1974 Gunderup-Gistrup Alborg 1975 Syd
5.0 4.8
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4.6 4.1
.
.
.
.
.
.
.
.
.
.
.
.
RMS/o0 .
.
.
.
.
.
.
.
.
.
.
.
0.92 0.85
5.2
5.7
1.10
4.7 6.0
4.2 4.2
0.89 0.70
4.6 5.0
4.1 4.8
0.89 0.96
5.6 4.1
5.2 3.1
0.93 0.76
5.0
4.9
0.98
5.2
4.0
0.77 mean: 0.89
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
36
includes a standard error on the control measurement of 2.5 cm. If that is deducted it leaves 5.2 cm for the p h o t o g r a m m e t r y . The gross errors have been divided in t w o groups, one for numbering errors and one for other gross errors. The reason for this is t h a t while the numbering errors are normally f o u n d and corrected, other gross errors, suc~, as for instance measuring a white stone instead of the signal, mean t h a t the coordinates of the point are lost. Whether the size of the errors depends on the length of the measured distance has been tested by a ×2-test. The 0-hypothesis, which was independence, was not rejected on a 95% level. Finally I have set up a small table to compare a0 of the adjustment with RMS from the test. The quotient RMS/a0 stays fairly steady on 0.9. When judging the q u o t i e n t RMS/a0, one has of course to r e m e m b e r t h a t the blocks were performed following the same scheme, b u t bearing t h a t in mind o0 seems to give a good idea of the size of ~i~e standard error to be expected in the field. CONCLUSION
As a whole the tests have been succes~fful.The results correspond very well with the expectations, and the testshave been quite easy to carry out. It was for instance possible to check 3 blocks in Alborg in one week. For the Cadastral Service as the supervising authority the field work gave in addition valuable information about the quality of the work done by the private surveyors, e.g. the marking of the points and the identificationin the pictures. If;is therefore the intention to make similar tests in future densification jobs.
REFERENCES Ackermann, F., 1976. Photogrammetrische Netzverdichtung- Das Projekt Appenweier. N~.merische Photogrammetrie (III), Stuttgart. Bauer, H., 1974. Bundle adjustment with additional parameters -- Practical experiences. Commission III, I.SoP. Symposit, m Stuttgart 1974. Hul!, W.V., 1975. Control densification by analytic photogrammetry. Journal of the S~rveying and Mapping division, Oktober 1975. Kilpel~i, E., 1970. Theoretische Genauigkeitsuntersuchungen der in Finland angewandten analytischen Biindelausgleichungsmethode. Helsingfors, 1970. Malinen, R.P., 1969. Simulation in photogrammetry. Helsingfors, 1969. Tewinkel, G.C., 1971. Photogrammetric geodesy. Commission III, I.S.P. Symposium, London, 1971.
29
D E N S I F I C A T I O N O F T R I G O N O M E T R I C NETS - - P R A C T I C A L E X P E R I E N C E S WITH B U N D L E A D J U S T M E N T
JONNA HVIDEGAARD CaHunavej 19, 3450 Alleroed (Denmark) (Received May 10, 1977; revised and accepted January 13, 1978)
ABSTRACT Hvidegaard, J., 1979. Densification of trigonometric nets -- Practical experiences with bundle adjustment. Photogrammetria, 35: 29--36. Fixed-points for cadastral measurements have been coordinated by use of the bundleadjustment method. The coordination was done by densification of an existing 2-kin vet of triangulated points down to a density of approx. 400 m. The photo scale was 1:t~000--1:10000 and the overlap 60/30. The accuracy of 11 blocks, covering an area of 631 km 2, has been tested in the field by measuring distances between coordinated points. Approx. 850 points were checked and ~ave a standard error of 5 cm on a photogrammetric coordinated point.
BACKGROUND
P h o t o g r a m m e t r y has already been used for some years for cadastral purposes in Denmark. To a certain degree, p h o t o g r a m m e t r i c plans have folml~d the basis of n e w cadastral maps. Perhaps more interesting in this c o n n e c t i o n is the fact t h a t p h o t o g r a m m e t r i c a l l y coordinated fixed-points are being used for cadastral measurements. The Geodetic Institute of D e n m a r k is responsible for t h e triangulation of higher order. The institute establishes points d o w n to a density of approx. 2 km. Further densification is left to t h e Cadastral Service and private surveyors. According to official regulations, t h e surveyors have to tie n e w cadastral m e a s u r e m e n t s to fixed-points w h e n these are located w i t h i n a distance of 200 m (for measuring roads the limit is 500 m). This means in practice t h a t unless one has a n e t of p o i n t s with a d e n s i t y of approx. 400 m, pr.~blems m a y arise especially in t h e developing areas of larger towns. Also, local authorities have a professional interest in t h e develoj~ing areas of the towns. One of t h e m a i n jobs for t h e p h o t o g r a m m e t r i c f i n n s is to p r o d u c e technical plans o n t h e scale 1 : 1 0 0 0 for the municipalities. The need for ground control for t h e compilation o f these plans corresponds very well w i t h t h e earlier m e n t i o n e d 400 rn net. T h e n e t is f u r t h e r m o r e useful for the local technical a d m i n i s t r a t i o n for m a p revision and setting o u t p~lrposes.
30
The jobs that will be presented in this paper are all the result of cooperation between a state authority, namely the Cadastral Service, a private photogrammetric firm, the local municipality: and the local private surveyor. THE PHOTOGRAMMETRIC
TRIANGULATION
Up to 1970 the only photogrammetric triangulation method used for the kind of jobs described was the Anblock, with models measured in analogue instruments such as A8, A7 and Simplex III. This method is still in use for smaller blocks and gives sufficiently good results with a photo scale of 1:4000 or 1: 5000. In 1970 the first test block in Denmark using bundle adjustment was made. The measuring and the calculations were done in Finland at the Technical Uniw~rsity of Helsinki. The results were promising, and since then some 50 jobs covering approx. 2000 km 2 have been performed, mainly in Finland but lately also in Denmark. All the jobs mentioned in this report were carried out in Finland. The pictures were measured on a Zeiss PSK comparator using glaswdiapositives and the calculations were made with the Finnish triangulation programme. Prior to the adjustment the pictures were corrected for: (1) film distortion (using affin transformation on the fiducial marks), (2) lens distortion (radial), (3) refraction, and (4 } earth curvature. Cr:iteria had to be established for the practical execution. When we started only very little had been published about practical results of point densification by aerial triangulation, and bundle adjustment was not yet very widely used. An early report was given by G.C. Tewinkel (U.S.A.) at the commission III symposium in London 1971 (Tewinkel, 1971). Since then a lot of things have been happening in that field. The development in the U.S.A. is described by W.V. Hull (1975), and in Germany e.g. tests using the Anblock method on models computed from comparator-measurements have been carried out in Stuttgart (Ackermann, 1976) and reports on bundle adjustment axe given by H. Bauer (1974) from Hannover. But 1970 was still ~airly early in this connection so we had to set our standards mainly on the basis of theoretical investigations (Malinen, 1969; Kilpel~i, 1970 ). The intention was to end up with a standard point error (x/n,2x + r~y ) of 5 cm on the ground, and after many considerations the following l~nes of direction were proposed: (1) Photo scale between 1:8000 and 1:10000. The predicted accuracies of the bundle-adjustment were 4--6 ~m in photo scale. (2) The cameras had to be the ordinary wide-angle cameras of the photogrammetric firms (c - 15 cm) and the film the normally used black and white panchromatic.
31
(3) Overlap q50/30 was chosen. Certainly, 60/60 would form a stronger block (Malinen, 1969; Tewinkel, 1971), but as the improvement is mainly on the Z-coordinate, and considering the increase in number of photographs in a block, 60/30 was agreed upon. In some cases 80% forward overlap was photographed. Not all the pictures were used in the block, but selections were done in order to "get d o w n " into streets, to get pictures in a good position in one strip compared to the next strip, or to fortify the block in weak areas by including extra pictures. (4) The distribution of ground control points was chosen according to the following scheme: Planimetric control along the perimeter of the block with a mutual distance of 4 X base. Height control as a net covering the whole block, the density being 2 X base. These figures are recommended by Dr. Kilpel~i from the Technical University of Finland in his investigation using simulated bloc~;s (Kilpel~i, 1970). Remembering the 2-kin net of triangulated points already existing in Denmark, the figures outlined the prospect of never having to measure anything but vertical control points in the field. These expectations have only been fulfilled to a certain extent. In a block it will normally be necessary to measure horizontal control points in 2--3 positions. The vertical controls all have to be measured and in spite of the fact th,~t the Z-coordinate is only of minor interest, at least from a cadastral point of view~ ~t was agreed to use the recommended net. (5) The accuracy of the triangulated points was stated by the Geodetic Institute in the following way: The maximum error on a distance between two n,~ighbouring points is 10 cm. As to the accuracy of the vertical control points the stavdard error was predicted to be 2--3 cm. (6) For targets white plates of 40 X 40 cm were chosen and a black contrast o~Yat least 15 cm around the signal was recommended. All ground control points should have extra signals (Fig. 1) first of all to ensure the identification in the pictures. (7) Artificial points (marked in the emulsion) were abandoned mainly because of unfavorable experiences from Anblock jobs. Where extra passpoints measured d i s t a n c e s
extra signal
control point
extra signal
measured d i s t a n c e
Vq control point Fig. 1
direction to knovn point
extra signal
32
were needed, either signals were set out in advance in the predicted side-lap and perimeter, or natural points were measured in the comparator. Broadly speaking these lines have been followed in the reported jobs. TEST Having made a number of blocks with the new method it seemed natural to check whether the results were in accordance with the expectations. Also, the possibilityof reaching the goal of 5 c m in standard error had been questioned. In order to certify an accuracy of 5 cm, a very exact geodetic measurement is required. At the same time the test should be fairly easy to carry out since a secondary aim of the investigation was to see whether a test could be done in a way that would make it reasonable to include it as a permanent part of future densification jobs. As the standard error of a distance can be shown to be equal to the standard error of a point, under the assumption of independence between the coordinates, measurement of distances would give the wanted result directly. Furthermore, the very simple geodetic " n e t " would give no error-propagation, and by using electronic distmlce-measuring equipment (EDM) the measurements could be of high accuracy. The standard error one gets by using distances is the relative one, but this is also the error of major interest here, as the coordinated points are going to be used for cada~tral measurements in the classical way. Having decided to use distances, the next problem was how to plan the field work. To allow the use of the normal distribution, the elements (these being the differences between the measured distance and the same distance calculated from the photogrammetric coordinates) must be independent. If one uses EDM the easiest way to g~t many controls would be to measure several distances from the same station, but then the elements are not independent. However, measuring only one distance from each point would increase the control work and the costs considerably. The actual work was done as a compromise between these two extremes, and calculations afterwards showed that *.he correlation was hardly ever significant. In all the jobs but one, the measured distances have been regarded as error-free. This is of course a point where one has to be careful. In the start of the collection of controls we also intended to use distances measured by the local su~leyors during their normal work. It appeared later that the standard error here (based on the remeasurement of 118 distances) was approx. 5 cm, which is the same as the expected error to be controlled. Out of 40 double measurements (never from the same station) the standard error on a distance measured by the testing group is computed to be just under 1 era.
33
0 C~
c~
C) 0 ,°
,°
o,
°°
°°
°°
°.
°°
°°
°°
°°
s~ "7'
I
I
II
I
c~
C)
pm~
C~
.=.
im=l
r.T.l
34
, ° , . ° °
O
O
O
~
. , °
O
O O O O ~ O
~
O
O
~
~
O
O
~00
O
O
N
N
NN
~
c~
O
O
~-~ ÷ ÷
~ +
÷
r,D 0 3
~.
03
E
,
~+~
~ ÷ ÷ +
÷÷
~'~
0
A ~
O
4-"
O
<
,~,<
,<
<
~<
<
<
35
It has to be m e n t i o n e d t h a t quite a few of the distances were in fact measured w i t h steel-tape, b u t as it appears from Table II t h e y were all u n d e r 10 m. These short dista:lces date f r o m double-signalized points where b o t h t h e point itself and t h e extra signal have b e e n coordinated. RESULTS The results are presented in Tables I and II, the firstone dealing with the actual flight mission and the calculations, the second with the control measurement. As can be seen from Table I, the side-lap and the photo scale vary to some extent. When a c o n t r a c t is set up for a flight program, a variation of + 10% is usually allowed in t h e side-lap. Nevertheless, some of the blocks on the list seem to have been p h o t o g r a p h e d in rough weather. As to the p h o t o scale it has to be m e n t i o n e d t h a t right f r o m the start one of the p h o t o g r a m m e t r i c firms wanted to use 1:8000 instead of 1:10000. The same firm uses 1 : 4 0 0 0 for low flying w h e r e t h e others prefer 1:5000. Therefore, t h e figures in the table should n o t solely be e x p o u n d e d as a growing confidence in the m e t h o d . T h e table does n o t tell a n y t h i n g a b o u t t h e distribution of t h e ground control points. An investigation showed t h a t c o m p a r e d with the r e c o m m e n d e d distribution, there were m o r e horizontal controls (mainly points inside the block) b u t less vertical controls (the net being closer to 3 × base t h a n to 2 × base). In Table II it has to be noticed t h a t t h e standard error of one of the tests TABLE III Block
Adjustment
Contro~ RMS (cm)
oo
(ca) .
Arhus 1971 Alborg 1971 Jersie 1971 Arhus 1972 Alborg 1972 Ellidsh~j Arhus 1973 Alborg 1973 Ajstrup HCje T~strup 1973 Alborg 1973 N~$rholm Alborg 1974 Gunderup-Gistrup Alborg 1975 Syd
5.0 4.8
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4.6 4.1
.
.
.
.
.
.
.
.
.
.
.
.
RMS/o0 .
.
.
.
.
.
.
.
.
.
.
.
0.92 0.85
5.2
5.7
1.10
4.7 6.0
4.2 4.2
0.89 0.70
4.6 5.0
4.1 4.8
0.89 0.96
5.6 4.1
5.2 3.1
0.93 0.76
5.0
4.9
0.98
5.2
4.0
0.77 mean: 0.89
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
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.
.
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.
36
includes a standard error on the control measurement of 2.5 cm. If that is deducted it leaves 5.2 cm for the p h o t o g r a m m e t r y . The gross errors have been divided in t w o groups, one for numbering errors and one for other gross errors. The reason for this is t h a t while the numbering errors are normally f o u n d and corrected, other gross errors, suc~, as for instance measuring a white stone instead of the signal, mean t h a t the coordinates of the point are lost. Whether the size of the errors depends on the length of the measured distance has been tested by a ×2-test. The 0-hypothesis, which was independence, was not rejected on a 95% level. Finally I have set up a small table to compare a0 of the adjustment with RMS from the test. The quotient RMS/a0 stays fairly steady on 0.9. When judging the q u o t i e n t RMS/a0, one has of course to r e m e m b e r t h a t the blocks were performed following the same scheme, b u t bearing t h a t in mind o0 seems to give a good idea of the size of ~i~e standard error to be expected in the field. CONCLUSION
As a whole the tests have been succes~fful.The results correspond very well with the expectations, and the testshave been quite easy to carry out. It was for instance possible to check 3 blocks in Alborg in one week. For the Cadastral Service as the supervising authority the field work gave in addition valuable information about the quality of the work done by the private surveyors, e.g. the marking of the points and the identificationin the pictures. If;is therefore the intention to make similar tests in future densification jobs.
REFERENCES Ackermann, F., 1976. Photogrammetrische Netzverdichtung- Das Projekt Appenweier. N~.merische Photogrammetrie (III), Stuttgart. Bauer, H., 1974. Bundle adjustment with additional parameters -- Practical experiences. Commission III, I.SoP. Symposit, m Stuttgart 1974. Hul!, W.V., 1975. Control densification by analytic photogrammetry. Journal of the S~rveying and Mapping division, Oktober 1975. Kilpel~i, E., 1970. Theoretische Genauigkeitsuntersuchungen der in Finland angewandten analytischen Biindelausgleichungsmethode. Helsingfors, 1970. Malinen, R.P., 1969. Simulation in photogrammetry. Helsingfors, 1969. Tewinkel, G.C., 1971. Photogrammetric geodesy. Commission III, I.S.P. Symposium, London, 1971.