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Recommendations
86 Recommendations presented at the Ottawa-Conference by Prof. B. H A L L E R T . For the future performance of aerial triangulation the following recom~endations are suggested. The recommendations are mainly a summary of the p a p e r "Determination and correction of systematic errors in the fundamental operations of aerial triangulation" by B. Hallert, Stockholm 70, Sweden. 1. The systematic non-projective deformations of the bundles of r a y s of the central projections at the photography and at the reconstructions should he carefully investigated under real working conditions. 1.1. The aerial camera should he tested with the aid of photography of grids from high buildings, preferably towers. I f vertical photography cannot he arranged, also oblique photographs can be used. In such cases the grid on the ground should be constructed as a perspective grid in order to obtain regular grids around the principal point of the photographs. The camera should be equipped as during real photography from the air. The photographic t r e a t m e n t of the negatives (films or plates) should be exactly as in practical work. A t least five but preferably ten individual photographs should be taken during these tests. The measurements and computations should be performed in accordance with the grid method. In this way a very reliable test of the normal performance of the camera and of the systematic non-projective deformations of the photographs and the inevitable variations will be obtained. The standard error of the image coordinate measurements, determined in accordance with the method of the least squares will indicate the limitation of the photographic procedure from a geometrical point of view. 1.2. It is desirable t h a t the camera he tested from the air with the grid method. The grid should be constructed for the actual flying altitude. In this way the systematic nonprojective deformations of the photographs during real photography from the air including all possible sources of errors will be determined. At least five individual photographs should be tested. Vector diagrams showing the residual errors should be constructed. If such tests from the air cannot he arranged, the y-parallax method should be used for the tests of the systematic non-projective deformations of the photographs. Normal stereoscopic photographs should be photographed from the actual altitude over areas with moderate elevation differences and good details. F r o m measurements of y-parallaxes in suitably located points (in particular in nine or fifteen regularly located points and symmetrical points along the fundamental circles) and simple computations the most important systematic non-projective deformations of the photographs can be determined. In particular, the standard error of the y-parallax measurements as computed in accordance with the method of the least squares will indicate the limitation of the photogrammetric procedure. In application of the y-parallax method, the influence of the earth's curvature has to be added to the determined radial distortion curve. The y-parallax method should be applied to a t least five pairs of photographs, taken under varying outer circumstances (different days, different film rolls etc.). The measurements of the y-parallaxes can be performed with so simple instruments as mirror stereoscope and parallax bar, provided t h a t the longitudinal and transversal inclinations of the photographs are less than about 1 °. In general a well adjusted instrument with mechanical projection can be used for the measurements. In instruments where no bytranslation is present the y-parallaxes can be measured with one of the co-screws. Stereoscopic measurements of the parallaxes should be preferred.
87 2. The systematic non-projective errors of the plotting i n s t r u m e n t s should be determined with the aid of m e a s u r e m e n t s of c a r e f u l l y tested glass grids, projected t h r o u g h t h e i n s t r u m e n t according to the grid method. In p a r t i c u l a r the i n s t r u m e n t should be tested for v a r y i n g base and elevation settings. The residual i n s t r u m e n t a l errors should be recorded as vector d i a g r a m s . Stereocomparators should be t r e a t e d in a similar way. 3. The combined effect" of the s y s t e m a t i c non-projective d e f o r m a t i o n s of the aerial test p h o t o g r a p h s a n d of the i n s t r u m e n t s should be checked by direct m e a s u r e m e n t s . F r o m the i n s t r u m e n t a l tests and the r e s u l t i n g vector d i a g r a m s , corrections to coordinates and p a r a l l a x e s can be determined for application to the t r i a n g u l a t i o n procedure. 4. In all stereoscopic models of the t r i a n g u l a t i o n procedure the residual y - p a r a l l a x e s should be m e a s u r e d and recorded after the absolute orientation (scale transfer) in a~ least nine and p r e f e r a b l y fifteen s y m m e t r i c a l l y located model points. The m e a s u r e m e n t s should be p e r f o r m e d stereoscopically and the r e a d i n g s should be m a d e by t h e recorder (not by the operator!). If the p a r a l l a x m e a s u r e m e n t s cannot be p e r f o r m e d in a n ideal point, two or preferably f o u r s y m m e t r i c a l l y around the point located details can be used for the p a r a l l a x m e a s u r e m e n t s . The average of the f o u r p a r a l l a x m e a s u r e m e n t s is t h e n used as the p a r a l l a x in the ideal point. Other discrepancies (in p a r t i c u l a r in the scale t r a n s f e r points) should be n u m e r i c a l l y m e a s u r e d a n d recorded in each model. 5. F r o m m e a s u r e m e n t s of t h e s u g g e s t e d type, the a c c u r a c y conditions of the actual aerial t r i a n g u l a t i o n can be theoretically determined. I f t h e principles of the n u m e r i c a l corrections are applied to the p r e l i m i n a r y results of the t r i a n g u l a t i o n , the h i g h e s t possible a c c u r a c y can be expected and t h i s accuracy can be e s t i m a t e d with the aid of the s t a n d a r d e r r o r s of the f u n d a m e n t a l operations and the corresponding weight n u m b e r s f r o m the used a d j u s t m e n t procedure. Up to now a v e r y good a g r e e m e n t between the theoretical and the practical accuracy h a s been found in a n u m b e r of tests. As a n example the Controlled t e s t s Oberriet 1956 can be mentioned. It would be h i g h l y desirable t h a t special t e s t s of aerial t r i a n g u l a t i o n s be p e r f o r m e d according to these suggestions in order to check the theoretical relations. Considerable increase of the a c c u r a c y and stability of aerial t r i a n g u l a t i o n s can doubtless be expected. I n f o r m a t i o n on all technical details of the s u g g e s t e d procedures is to be found in the I n t e r n a t i o n a l Archives of P h o t o g r a m m e t r y , Vol. XII, 1956.
Discussion of Dr. Hallert's paper (presented by Dr. P. O. F a g e r h o l m ) .
Dr. Schmid: I recognize the necessity of i n v e s t i g a t i n g the f u n d a m e n t a l p a r a m e t e r s of p h o t o g r a m m e t r i c m e a s u r e m e n t s . I doubt however t h a t the proposed method of steel tower observations and p h o t o g r a p h y is adequate. The given geometrical c o n f i g u r a t i o n s will produce p h o t o g r a p h s at a scale of 1 : 1000 for C = 0.1 m to 1 : 500 for C = 0.21 m. Ass u m i n g the r a n d o m error of the geodetic reference points on the g r o u n d to be -+- 2 to 3 m m (page 3 of the a u t h o r ' s p a p e r ) , which is excellent, the corresponding r a n d o m errors in the plane of the p h o t o g r a p h r e s u l t i n g f r o m this cause alone will be ± 3 to 6 microns. To obtain a sufficiently stable position for the perspective centre on the horizontal b a r of the steel tower would seem to be v e r y difficult indeed, not to mention the problem of definition a n d d e t e r m i n a t i o n of t h a t hypothetical point which will emerge in the analytical reduction procedure as the "centre of projection". F u r t h e r m o r e , 125 m e t r e s seems to be m u c h too short for other reasons. Even if a s h a r p image is produced, the photographic image will be displaced relative to the image of a point in the s a m e direction b u t a t a g r e a t e r distance. If a point source of light were photographed a t such a short distance coma effects would probably be noticeable.
87 2. The systematic non-projective errors of the plotting i n s t r u m e n t s should be determined with the aid of m e a s u r e m e n t s of c a r e f u l l y tested glass grids, projected t h r o u g h t h e i n s t r u m e n t according to the grid method. In p a r t i c u l a r the i n s t r u m e n t should be tested for v a r y i n g base and elevation settings. The residual i n s t r u m e n t a l errors should be recorded as vector d i a g r a m s . Stereocomparators should be t r e a t e d in a similar way. 3. The combined effect" of the s y s t e m a t i c non-projective d e f o r m a t i o n s of the aerial test p h o t o g r a p h s a n d of the i n s t r u m e n t s should be checked by direct m e a s u r e m e n t s . F r o m the i n s t r u m e n t a l tests and the r e s u l t i n g vector d i a g r a m s , corrections to coordinates and p a r a l l a x e s can be determined for application to the t r i a n g u l a t i o n procedure. 4. In all stereoscopic models of the t r i a n g u l a t i o n procedure the residual y - p a r a l l a x e s should be m e a s u r e d and recorded after the absolute orientation (scale transfer) in a~ least nine and p r e f e r a b l y fifteen s y m m e t r i c a l l y located model points. The m e a s u r e m e n t s should be p e r f o r m e d stereoscopically and the r e a d i n g s should be m a d e by t h e recorder (not by the operator!). If the p a r a l l a x m e a s u r e m e n t s cannot be p e r f o r m e d in a n ideal point, two or preferably f o u r s y m m e t r i c a l l y around the point located details can be used for the p a r a l l a x m e a s u r e m e n t s . The average of the f o u r p a r a l l a x m e a s u r e m e n t s is t h e n used as the p a r a l l a x in the ideal point. Other discrepancies (in p a r t i c u l a r in the scale t r a n s f e r points) should be n u m e r i c a l l y m e a s u r e d a n d recorded in each model. 5. F r o m m e a s u r e m e n t s of t h e s u g g e s t e d type, the a c c u r a c y conditions of the actual aerial t r i a n g u l a t i o n can be theoretically determined. I f t h e principles of the n u m e r i c a l corrections are applied to the p r e l i m i n a r y results of the t r i a n g u l a t i o n , the h i g h e s t possible a c c u r a c y can be expected and t h i s accuracy can be e s t i m a t e d with the aid of the s t a n d a r d e r r o r s of the f u n d a m e n t a l operations and the corresponding weight n u m b e r s f r o m the used a d j u s t m e n t procedure. Up to now a v e r y good a g r e e m e n t between the theoretical and the practical accuracy h a s been found in a n u m b e r of tests. As a n example the Controlled t e s t s Oberriet 1956 can be mentioned. It would be h i g h l y desirable t h a t special t e s t s of aerial t r i a n g u l a t i o n s be p e r f o r m e d according to these suggestions in order to check the theoretical relations. Considerable increase of the a c c u r a c y and stability of aerial t r i a n g u l a t i o n s can doubtless be expected. I n f o r m a t i o n on all technical details of the s u g g e s t e d procedures is to be found in the I n t e r n a t i o n a l Archives of P h o t o g r a m m e t r y , Vol. XII, 1956.
Discussion of Dr. Hallert's paper (presented by Dr. P. O. F a g e r h o l m ) .
Dr. Schmid: I recognize the necessity of i n v e s t i g a t i n g the f u n d a m e n t a l p a r a m e t e r s of p h o t o g r a m m e t r i c m e a s u r e m e n t s . I doubt however t h a t the proposed method of steel tower observations and p h o t o g r a p h y is adequate. The given geometrical c o n f i g u r a t i o n s will produce p h o t o g r a p h s at a scale of 1 : 1000 for C = 0.1 m to 1 : 500 for C = 0.21 m. Ass u m i n g the r a n d o m error of the geodetic reference points on the g r o u n d to be -+- 2 to 3 m m (page 3 of the a u t h o r ' s p a p e r ) , which is excellent, the corresponding r a n d o m errors in the plane of the p h o t o g r a p h r e s u l t i n g f r o m this cause alone will be ± 3 to 6 microns. To obtain a sufficiently stable position for the perspective centre on the horizontal b a r of the steel tower would seem to be v e r y difficult indeed, not to mention the problem of definition a n d d e t e r m i n a t i o n of t h a t hypothetical point which will emerge in the analytical reduction procedure as the "centre of projection". F u r t h e r m o r e , 125 m e t r e s seems to be m u c h too short for other reasons. Even if a s h a r p image is produced, the photographic image will be displaced relative to the image of a point in the s a m e direction b u t a t a g r e a t e r distance. If a point source of light were photographed a t such a short distance coma effects would probably be noticeable.