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Some experiments on semi-analytical triangulation
273
Some Experiments on Semi-analytical Triangulation by Prof. G. I N G H I L L E R I Politecnico di Milano, Italy SUMMARY. This p a p e r will appear in full in the Archives of the I.S.P.-Congress in Lisboa, September 1964. The paper describes a method of triangulation with independent models, which may be executed on precision plotters as for instance, the Stereosimplex Santoni, the Wild A8. The Y- and Z-components o f the i n s t r u m e n t base, if present, are kept in their zeropositions. The X-component is set on a value which remains constant for the whole strip and is selected so t h a t the models have optimum large scale. For the relative orientation, ;gl, ~2, cP1, Q~2 and w2 (or o>1) are used. A f t e r the r e l a t i v e orientation the modelcoordinates of the pass-points, tie-points and, if available, the control points, are read and/or recorded. When model i - - 1 , i is finished, photo i is t r a n s f e r r e d from the righthand camera to the left-hand camera, and photo i + 1 is introduced into the right-hand camera. There is no t r a n s f e r of scale in the operational procedure. Each model, therefore, has its own individual scale and orientation in space. The connection of each model to its predecessor, so t h a t one continuous chain of models is realised, is done by computation outside the instrument. For the connection of model (i, i + 1) to model ( i - - 1 , i), the passpoints in the supratap of these two models, together with the perspective centre (or "exposure station") of photo i, are used. Actually, these passpoints wit] be selected in the common photo i and will be situated (approximately) in a line parallel to Y and passing through the principal point of photo i. Usually, two wingpoints (A and B) and one central point (C) are used for the connection. It will be clear t h a t the common triangle 0lAB more t h a n suffices to connect model (i, i + 1) to model ( i - - 1 , i)~ because the connection includes seven unknowns (viz. the three rotations, the three translations and the scale of model i, i ÷ 1 relative to model i - - l , i) and the three points 0~, A and B supply 3 X 3 coordinates thus 9 data. The coordinates (X, Y, Z) of the two perspective centres in the fixed system of model coordinates are constant all through the strip. They m a y be determined from grid plate observations, f i r s t with the lowest possible and then w i t h the highest possible projection distance. The numerical connection has been programmed on the IBM 7040 computer. The time f o r the computation of a strip of 10 models (where model 2 is connected to model 1 and the model coordinates observed in model 2 are t r a n s f o r m e d into the system of model 1, where model three is connected to the t r a n s f o r m e d model 2, etc.) is about 1 minute on the IBM 7040. Computation on a desk machine probably would require the same time as t h a t needed for the instrumental triangulation itself. I f an electronic computer is available, it would be possible to reduce the instrumental work still f u r t h e r , and to improve the accuracy, by computing corrections to the observed model coordinates as functions of observed residual Y-parallaxes. Also, corrections could be applied f o r distortion, atmospheric refraction, film shrinkage, etc. These possibilities, however, have not yet been realised. At present, the computation programme used for the a d j u s t m e n t of the semianalytical strips is the s a m e as t h a t used for anaiogue or analytical triangulation executed at the Milano Centre.
Results o f tests. Some experiments have been performed on the strips 2 -
6--1
and 2 -
6-
4 of
[15]
274
Photogvammetria, XIX, No. 7
the O E E P E / C o m m i s s i o n B/Reichenbach test block. The photos have been taken with the RC 7 glass plate camera (14 X 14 cm, c = 10 cm) ; flying height: 1200 metres above the t e r r a i n (1 : 12000) ; ground height differences of about 20% of the flying height. 1. The mean square values of the discrepancies in X, Y, Z in the four points (O, A, B, C) used for the analytical connection, between the successive models, were about 7, 24 and 26 microns (in the scale of the photos) respectively. These values show the efficiency of the conne'ctions between the models. 2. Practical experiments confirmed w h a t could have been derived theoretically, viz. t h a t errors in the determination of the coordinates (X, Y, Z) of the two perspective centres (by grid plate observations, see earlier) cause systematic errors in the model coordinates t h a t can be perfectly eliminated with a parabolic adjustment. 3. The strip coordinates were subjected f i r s t to a linear and then to a parabolic t r a n s formation. F o r the linear transformation, four control points have been used; two at each end of the strips. For the parabolic t r a n s f o r m a t i o n nine control points have been used; three a t the beginning, three in the middle and t h r e e at the end of the strips. A table is given with the results. A f t e r linear t r a n s f o r m a t i o n , relatively large e r r o r s remain: in the Z-coordinates even errors of several metres. The errors, however, are highly correlated and disappear to a large extent a f t e r parabolic adjustment. A f t e r parabolic adjustment, the s t a n d a r d deviations in the X, Y, Z of the check points are about 25 cm, 23 cm and 30 cm respectively (in the scale of t h e terrain). The comparison with the results of the triangulations of the same strips, executed by other organisations on other i n s t r u m e n t s in the framework of the O E E P E shows t h a t the precision and accuracy of the semi-analytical triangulation executed on the Stereosimplex III, is perfectly comparable to t h a t obtained by the other methods.
[16]
Some Experiments on Semi-analytical Triangulation by Prof. G. I N G H I L L E R I Politecnico di Milano, Italy SUMMARY. This p a p e r will appear in full in the Archives of the I.S.P.-Congress in Lisboa, September 1964. The paper describes a method of triangulation with independent models, which may be executed on precision plotters as for instance, the Stereosimplex Santoni, the Wild A8. The Y- and Z-components o f the i n s t r u m e n t base, if present, are kept in their zeropositions. The X-component is set on a value which remains constant for the whole strip and is selected so t h a t the models have optimum large scale. For the relative orientation, ;gl, ~2, cP1, Q~2 and w2 (or o>1) are used. A f t e r the r e l a t i v e orientation the modelcoordinates of the pass-points, tie-points and, if available, the control points, are read and/or recorded. When model i - - 1 , i is finished, photo i is t r a n s f e r r e d from the righthand camera to the left-hand camera, and photo i + 1 is introduced into the right-hand camera. There is no t r a n s f e r of scale in the operational procedure. Each model, therefore, has its own individual scale and orientation in space. The connection of each model to its predecessor, so t h a t one continuous chain of models is realised, is done by computation outside the instrument. For the connection of model (i, i + 1) to model ( i - - 1 , i), the passpoints in the supratap of these two models, together with the perspective centre (or "exposure station") of photo i, are used. Actually, these passpoints wit] be selected in the common photo i and will be situated (approximately) in a line parallel to Y and passing through the principal point of photo i. Usually, two wingpoints (A and B) and one central point (C) are used for the connection. It will be clear t h a t the common triangle 0lAB more t h a n suffices to connect model (i, i + 1) to model ( i - - 1 , i)~ because the connection includes seven unknowns (viz. the three rotations, the three translations and the scale of model i, i ÷ 1 relative to model i - - l , i) and the three points 0~, A and B supply 3 X 3 coordinates thus 9 data. The coordinates (X, Y, Z) of the two perspective centres in the fixed system of model coordinates are constant all through the strip. They m a y be determined from grid plate observations, f i r s t with the lowest possible and then w i t h the highest possible projection distance. The numerical connection has been programmed on the IBM 7040 computer. The time f o r the computation of a strip of 10 models (where model 2 is connected to model 1 and the model coordinates observed in model 2 are t r a n s f o r m e d into the system of model 1, where model three is connected to the t r a n s f o r m e d model 2, etc.) is about 1 minute on the IBM 7040. Computation on a desk machine probably would require the same time as t h a t needed for the instrumental triangulation itself. I f an electronic computer is available, it would be possible to reduce the instrumental work still f u r t h e r , and to improve the accuracy, by computing corrections to the observed model coordinates as functions of observed residual Y-parallaxes. Also, corrections could be applied f o r distortion, atmospheric refraction, film shrinkage, etc. These possibilities, however, have not yet been realised. At present, the computation programme used for the a d j u s t m e n t of the semianalytical strips is the s a m e as t h a t used for anaiogue or analytical triangulation executed at the Milano Centre.
Results o f tests. Some experiments have been performed on the strips 2 -
6--1
and 2 -
6-
4 of
[15]
274
Photogvammetria, XIX, No. 7
the O E E P E / C o m m i s s i o n B/Reichenbach test block. The photos have been taken with the RC 7 glass plate camera (14 X 14 cm, c = 10 cm) ; flying height: 1200 metres above the t e r r a i n (1 : 12000) ; ground height differences of about 20% of the flying height. 1. The mean square values of the discrepancies in X, Y, Z in the four points (O, A, B, C) used for the analytical connection, between the successive models, were about 7, 24 and 26 microns (in the scale of the photos) respectively. These values show the efficiency of the conne'ctions between the models. 2. Practical experiments confirmed w h a t could have been derived theoretically, viz. t h a t errors in the determination of the coordinates (X, Y, Z) of the two perspective centres (by grid plate observations, see earlier) cause systematic errors in the model coordinates t h a t can be perfectly eliminated with a parabolic adjustment. 3. The strip coordinates were subjected f i r s t to a linear and then to a parabolic t r a n s formation. F o r the linear transformation, four control points have been used; two at each end of the strips. For the parabolic t r a n s f o r m a t i o n nine control points have been used; three a t the beginning, three in the middle and t h r e e at the end of the strips. A table is given with the results. A f t e r linear t r a n s f o r m a t i o n , relatively large e r r o r s remain: in the Z-coordinates even errors of several metres. The errors, however, are highly correlated and disappear to a large extent a f t e r parabolic adjustment. A f t e r parabolic adjustment, the s t a n d a r d deviations in the X, Y, Z of the check points are about 25 cm, 23 cm and 30 cm respectively (in the scale of t h e terrain). The comparison with the results of the triangulations of the same strips, executed by other organisations on other i n s t r u m e n t s in the framework of the O E E P E shows t h a t the precision and accuracy of the semi-analytical triangulation executed on the Stereosimplex III, is perfectly comparable to t h a t obtained by the other methods.
[16]