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Aerotriangulation by independent models: A comparison with other methods
Photogrammetria
-
Elsevier Publishing Company, Amsterdam - Printed in The Netherlands
A E R O T R I A N G U L A T I O N BY I N D E P E N D E N T MODELS: A C O M P A R I S O N WITH OTHER METHODS l V. A. W I L L I A M S
AND H. H. B R A Z I E R
Directorate of Overseas Surveys, Tolworth, S.rrey (Great Britain)
(Received May 17, 1966)
SUMMARY The method of aerotriangulation by independent models is compared with analytical methods using comparators, from the standpoint of the timing of the change of form in data-flow and of instrumentation; a short account of the development of the technique is given.
The choice of a production method for aerotriangulation, from the varied techniques and instrumentations which have been developed, is a problem which exercises many photogrammetrists. In the first part of this paper we shall deal with certain of the factors which influence this choice from two points of view, but as an introduction a few general remarks about aerotriangulation are made. Aerotriangulation can be considered as starting with a pattern of points on a piece of terrain and ending with an array of points each one having assigned to it a position relative to a grid; this array having a distribution suitable for forming the basis of the map-plotting operation. As long as comparatively low-accuracy requirements are specified for the final mapping a production train based on graphical analogue forms will suffice but as soon as a higher accuracy is specified the whole of the information has to be digitised somewhere along the production train. The photogrammetrist is normally given a set of photographs of the terrain and a set of numbers (coordinates) which refer to selected points in it. Because of imperfections in both the photography and in the coordinates of selected control points, this original information represents an imperfect image of the reality of the patterns of points. Ignoring graphical analogue methods, the photogrammetrist usually attempts to build up a consistent set of numbers related to 1 Paper presented at the International Symposium on Spatial Aerotriangulation. February 28-March 24, 1966, University of Illinois, Ill., (U.S.A.). The Ministry of Overseas Development does not necessarily endorse opinions or recommendations made in this paper nor do they necessarily represent official policy. Photogrammetria
2! (1966) 95-99
96
V. A. W I L L I A M S
AND H. H. B R A Z I E R
the coordinated points from observations made on the photography and then to obtain one-to-one correspondence formulae between this set of numbers and the coordinates given. He then applies the formulae to assign coordinates to the array of points necessary for forming the photo models for map plotting. During the chain of production processes of all the techniques (except that of the graphical analogue) the photographic positions of all the points have to be changed from analogue form into digital form. Associated with this change is the choice of the appropriate instruments. Let us first consider three techniques from the standpoint of the timing of the change of form in data flow: (/) The stereocomparator technique changes the data into digits (recorded on punch tape or cards) after each point area is viewed through a stereoscope. (I1) Aerotriangulation based on observations made by means of a single plate measuring instrument introduces digits relatively later in the production train; after the points have been "transfer-marked" from one photograph to the others on which they appear. (Ill) The methods based on the adjustment of independent models call for the change from analogue to digital form even later in the proceedings; after the relative orientations of photographic models have been achieved. The stage at which the change in data form is made has several important consequences: (A) It is clear that the sooner digits are introduced the greater the chances of introducing numerical errors into the data. These numerical errors are not only liable to enter into the measurement data but also into the identification numbering of the points. From this point of view the later the transition to digits is made the better. (B) Defects in the photography can best be recognised by setting the models in relative orientation in an analogue plotting instrument. The earlier in the production train that such defects are isolated, the less time is wasted in making measurements and adjustment on bad data. Considering the argument above, technique (I11) offers distinct advantages over the other two: the transition fi'om analogue form is made later, it requires a minimum of ':tagging of data" and the analogue relative orientation is done earlier. To overcome partially the disadvantages in 1 and I1, checks and intermediate processes can be introduced bul these in turn result in the processes becoming tedious and time-consuming. Let us now consider the techniques from the standpoint of the instruments which are required: (1) The stereocomparator technique calls for an expensive instrument which is operated by a specialist and cannot be used for any other phase of the production train. In order to obtain a suitable accuracy it should operate at tolerances considerably lower than the levels necessary to produce the model in the final plotting process. (2) The technique based on single photo measurements is done in two phases. The first phase involves the marking of all the points selected to be measured. Photogrammetria,
21 ( 1 9 6 6 ) 95 9 9
AEROTRIANGULATION BY INDEPENDENT MODELS
97
Many points will fall on three photographs, some on as many as six. T o p e r f o r m this operation a "point transfer marker" must be used. To design an instrument which will not only allow a stereo-pointing on a point of detail, but also the precise physical placing of marks on two glass plates (by drilling or punching) so that they consistently fit a given measuring mark, is not an easy task. All such instruments which we have seen seem to have attracted criticism on one count or another. Before the technique can be said to be developed as a production method a successful "point transfer marker" must be produced capable of a high rate of output. There are a number of instruments available for measuring the plate coordinates of the point-marks, and one, at least, the Zeiss (Jena) 3030 coordinatemeasuring instrument with read-out, will perform the operation with a high production rate. The instrument is not cheap and cannot be used elsewhere in the production train. (3) The adjustment of independent models techniques requires a mininlum amount of preparation. Only the lateral lie-points need to be transferred between strips and their siting is usually so undemanding that points of firm detail can generally be used. The instrument required is a plotter fitted with a read-out to punched tape. The instrument which we have used with production efficiency is the Wild A8 with E K 5 a read-out. The A8 is regarded as a first order plotter, but will not perform aerotriangulation with "base in - base out" procedure. The instruments for methods 1 and 2 can be used only for aerotriangulation. In order to keep an even flow of production with instrumentation fully employed, a nice balance has to be maintained between aerotriangulation and plotting. To allow the expensive equipment of methods 1 and 2 to be under-employed is not only uneconomic but produces side-effects, e.g., the operators becoming out of practice in its efficient use. The production advantages of technique 3 arc especially attractive to the smaller mapping organizations possessing less than, say, twenty plotters. The imbalance between instrument output for aerotriangulation and that for plotting can be readily corrected by varying the proportion of the plotters being used for aerotriangulation as opposed to plotting. The first crude attempts by the Directorate of Overseas Surveys at the adjustment of independent models occurred in 1949 - 1951. At that time we were committed to supplying topographical maps at a scale of 1:50,000 of the catchment area of the Zambesi River for the Kariba D a m Project. Because of the sparseness of control, it was impossible to bridge on multiplex by the methods then in use. The Director (Brigadier M. Hotine) instructed that multiplex models were to be observed singly, scaled to a slotted template assembly, roughly leveled by topographic considerations and then joined by computational methods to give a continuous model surface which was to be finally oriented to fit the sparse ground control. The insight we gained during this project into the production difficulties involved led us to realise that in order to make such a method work we must (a) include the common perspective centres of adjacent models and (b) improve the means of handling the vast amount of digital data to be processed.
PhotogramnTetria,
21 (1966) 95 99
98
V. A. W I L L I A M S AND H. H. BRAZIER
With this salutary experience still fresh in our minds we were faced, in 1956, with having to produce aerotriangulation by some means other than classical analogue methods, as our only rather old first-order instrument capable of aerotriangulation at that time had broken down. It could be adjusted so as to produce a reasonably accurate answer "base-in" but not "base-out". This necessity mothered our first trials in which a laborious hand-machine arithmetic calculation was used. The acquisition of a Thompson--Watts plotter in 1958 allowed us to carry on with the development, but it was not until we procured a Wild A8 in 1961 (with an EK5a read-out at a later date) that we were able to use the method on a full production basis. Since then we have successfully performed aerotriangulation over some fifteen blocks of photography in a variety of terrain. Early in 1965, an opportunity arose to submit the method to an accuracy test against premarked ground control, using "reseau" photography which had been processed by the stereocomparator technique (WILLIAMS, 1965). Although it is difficult to compare production times of method 3 with those of 1 and 2 there is reason to believe that the latter are not as economical as the former in production costs. There is no difficulty in maintaining an output of five overlaps per 7-h day. The resulting accuracy of the test was not less than that of the analytical method. We have not had much experience in using plotters other than the Wild A8 for the production of aerotriangulation by the observation of independent models. We hope that plotters capable of dealing with super-wide-angle photography will soon be fitted with a suitable read-out. An instrument which might lend itself admirably to this purpose is the P.G.2 by Kern of Aarau. This instrument, which can produce surprisingly accurate analogue bridging for height, allows a rapid relative orientation to be performed. Owing to the design of the instrument, however, the coordinates of one of the perspective centres would change with each successive model, and would have to be introduced as a variable value into the tape, but the remainder of the operation could well develop into a rapid method for producing the data for topographic mapping. Another project which interests us is the correction of errors from slightly deformed photography. By analysing the model deformation in a controlled model we hope to be able to arrive at corrections which can be fed automatically into the computing programme at the same time as the observations. The development of "Aerotriangulation by the observation of Independent Models", which we have shortened to A.I.M. for the convenience of our staff in the Directorate, has been sporadic and spread over the years since both of the authors are engaged not so much in research and development as in the day to day production of maps. We have been aware of a climate of opinion which has influenced the development of A.I.M. THOMPSON (1964) mentioned the work of H. G. Fourcade who was working in 1926 to produce an instrument for the express purpose of triangulating in this way. THOMPSON (1959) gave formulae (subsequently improved by SCHUT, 1960) for use in obtaining the relationship of two sets of three dimensional coordinates. Photo~,,ramnTetria 21 (1966) 95-.99
AEROTRIANGULATION BY INDEPENDENT MODELS
99
INGHILLERI (1962--1964) gave an account of his work on this technique using a Stereosimplex Santoni plotter at the Delft meeting, and has reported on further work (INGIatLLERI, 1965). In the early 1950's the I.G.N. (Paris) were using a version of the adjustment of independent model technique. It has been well said that every scientific or technical advance rests on the shoulders of those who went before and the authors are particularly conscious of the truth of this saying in the case of A.I.M. We wish particularly to acknowledge ScHUT's (1960, p.35) equations which have greatly assisted the computational work involved in A.I.M.
REFERENCES INGHItLERI, G., 1964. Some experiments of semi-analytical triangulation. Photogrammetria, 19(7): 273-274. IN6mLLERI, ¢3, 1965. Contributions to the study of semi-analytical triangulation, ltalmapE.I.R.A. Chronicle, 1 2 : 5 7 - 7 2 SCHUT, G. H., 1960. On exact linear equations for the computation of the rotational elements of absolute orientation. Photogrammetria, 17(1): 34-37. THOMPSON, E. H., 1959. A method for the construction of orthogonal matrices. Photogrammetric Record, 3(13): 55-59. THOMPSON, E. H., 1964. Aerial triangulation by independent models. Photogrammetria, 19(7): 262-265. WILLIAMS. V. A. and BRAZIER, H. H., 1964 Aerotriangulation by the observation of independent models. Photogrammetria, 19(7): 275-278. WIt, L~AMS, V. A. and BRAZIER, H. H., 1965, The method of the adjustment of independent models. Photogrammetric Record, 5(26): 123-130.
PhotoL,rammetria 21 (11966) 95 99
-
Elsevier Publishing Company, Amsterdam - Printed in The Netherlands
A E R O T R I A N G U L A T I O N BY I N D E P E N D E N T MODELS: A C O M P A R I S O N WITH OTHER METHODS l V. A. W I L L I A M S
AND H. H. B R A Z I E R
Directorate of Overseas Surveys, Tolworth, S.rrey (Great Britain)
(Received May 17, 1966)
SUMMARY The method of aerotriangulation by independent models is compared with analytical methods using comparators, from the standpoint of the timing of the change of form in data-flow and of instrumentation; a short account of the development of the technique is given.
The choice of a production method for aerotriangulation, from the varied techniques and instrumentations which have been developed, is a problem which exercises many photogrammetrists. In the first part of this paper we shall deal with certain of the factors which influence this choice from two points of view, but as an introduction a few general remarks about aerotriangulation are made. Aerotriangulation can be considered as starting with a pattern of points on a piece of terrain and ending with an array of points each one having assigned to it a position relative to a grid; this array having a distribution suitable for forming the basis of the map-plotting operation. As long as comparatively low-accuracy requirements are specified for the final mapping a production train based on graphical analogue forms will suffice but as soon as a higher accuracy is specified the whole of the information has to be digitised somewhere along the production train. The photogrammetrist is normally given a set of photographs of the terrain and a set of numbers (coordinates) which refer to selected points in it. Because of imperfections in both the photography and in the coordinates of selected control points, this original information represents an imperfect image of the reality of the patterns of points. Ignoring graphical analogue methods, the photogrammetrist usually attempts to build up a consistent set of numbers related to 1 Paper presented at the International Symposium on Spatial Aerotriangulation. February 28-March 24, 1966, University of Illinois, Ill., (U.S.A.). The Ministry of Overseas Development does not necessarily endorse opinions or recommendations made in this paper nor do they necessarily represent official policy. Photogrammetria
2! (1966) 95-99
96
V. A. W I L L I A M S
AND H. H. B R A Z I E R
the coordinated points from observations made on the photography and then to obtain one-to-one correspondence formulae between this set of numbers and the coordinates given. He then applies the formulae to assign coordinates to the array of points necessary for forming the photo models for map plotting. During the chain of production processes of all the techniques (except that of the graphical analogue) the photographic positions of all the points have to be changed from analogue form into digital form. Associated with this change is the choice of the appropriate instruments. Let us first consider three techniques from the standpoint of the timing of the change of form in data flow: (/) The stereocomparator technique changes the data into digits (recorded on punch tape or cards) after each point area is viewed through a stereoscope. (I1) Aerotriangulation based on observations made by means of a single plate measuring instrument introduces digits relatively later in the production train; after the points have been "transfer-marked" from one photograph to the others on which they appear. (Ill) The methods based on the adjustment of independent models call for the change from analogue to digital form even later in the proceedings; after the relative orientations of photographic models have been achieved. The stage at which the change in data form is made has several important consequences: (A) It is clear that the sooner digits are introduced the greater the chances of introducing numerical errors into the data. These numerical errors are not only liable to enter into the measurement data but also into the identification numbering of the points. From this point of view the later the transition to digits is made the better. (B) Defects in the photography can best be recognised by setting the models in relative orientation in an analogue plotting instrument. The earlier in the production train that such defects are isolated, the less time is wasted in making measurements and adjustment on bad data. Considering the argument above, technique (I11) offers distinct advantages over the other two: the transition fi'om analogue form is made later, it requires a minimum of ':tagging of data" and the analogue relative orientation is done earlier. To overcome partially the disadvantages in 1 and I1, checks and intermediate processes can be introduced bul these in turn result in the processes becoming tedious and time-consuming. Let us now consider the techniques from the standpoint of the instruments which are required: (1) The stereocomparator technique calls for an expensive instrument which is operated by a specialist and cannot be used for any other phase of the production train. In order to obtain a suitable accuracy it should operate at tolerances considerably lower than the levels necessary to produce the model in the final plotting process. (2) The technique based on single photo measurements is done in two phases. The first phase involves the marking of all the points selected to be measured. Photogrammetria,
21 ( 1 9 6 6 ) 95 9 9
AEROTRIANGULATION BY INDEPENDENT MODELS
97
Many points will fall on three photographs, some on as many as six. T o p e r f o r m this operation a "point transfer marker" must be used. To design an instrument which will not only allow a stereo-pointing on a point of detail, but also the precise physical placing of marks on two glass plates (by drilling or punching) so that they consistently fit a given measuring mark, is not an easy task. All such instruments which we have seen seem to have attracted criticism on one count or another. Before the technique can be said to be developed as a production method a successful "point transfer marker" must be produced capable of a high rate of output. There are a number of instruments available for measuring the plate coordinates of the point-marks, and one, at least, the Zeiss (Jena) 3030 coordinatemeasuring instrument with read-out, will perform the operation with a high production rate. The instrument is not cheap and cannot be used elsewhere in the production train. (3) The adjustment of independent models techniques requires a mininlum amount of preparation. Only the lateral lie-points need to be transferred between strips and their siting is usually so undemanding that points of firm detail can generally be used. The instrument required is a plotter fitted with a read-out to punched tape. The instrument which we have used with production efficiency is the Wild A8 with E K 5 a read-out. The A8 is regarded as a first order plotter, but will not perform aerotriangulation with "base in - base out" procedure. The instruments for methods 1 and 2 can be used only for aerotriangulation. In order to keep an even flow of production with instrumentation fully employed, a nice balance has to be maintained between aerotriangulation and plotting. To allow the expensive equipment of methods 1 and 2 to be under-employed is not only uneconomic but produces side-effects, e.g., the operators becoming out of practice in its efficient use. The production advantages of technique 3 arc especially attractive to the smaller mapping organizations possessing less than, say, twenty plotters. The imbalance between instrument output for aerotriangulation and that for plotting can be readily corrected by varying the proportion of the plotters being used for aerotriangulation as opposed to plotting. The first crude attempts by the Directorate of Overseas Surveys at the adjustment of independent models occurred in 1949 - 1951. At that time we were committed to supplying topographical maps at a scale of 1:50,000 of the catchment area of the Zambesi River for the Kariba D a m Project. Because of the sparseness of control, it was impossible to bridge on multiplex by the methods then in use. The Director (Brigadier M. Hotine) instructed that multiplex models were to be observed singly, scaled to a slotted template assembly, roughly leveled by topographic considerations and then joined by computational methods to give a continuous model surface which was to be finally oriented to fit the sparse ground control. The insight we gained during this project into the production difficulties involved led us to realise that in order to make such a method work we must (a) include the common perspective centres of adjacent models and (b) improve the means of handling the vast amount of digital data to be processed.
PhotogramnTetria,
21 (1966) 95 99
98
V. A. W I L L I A M S AND H. H. BRAZIER
With this salutary experience still fresh in our minds we were faced, in 1956, with having to produce aerotriangulation by some means other than classical analogue methods, as our only rather old first-order instrument capable of aerotriangulation at that time had broken down. It could be adjusted so as to produce a reasonably accurate answer "base-in" but not "base-out". This necessity mothered our first trials in which a laborious hand-machine arithmetic calculation was used. The acquisition of a Thompson--Watts plotter in 1958 allowed us to carry on with the development, but it was not until we procured a Wild A8 in 1961 (with an EK5a read-out at a later date) that we were able to use the method on a full production basis. Since then we have successfully performed aerotriangulation over some fifteen blocks of photography in a variety of terrain. Early in 1965, an opportunity arose to submit the method to an accuracy test against premarked ground control, using "reseau" photography which had been processed by the stereocomparator technique (WILLIAMS, 1965). Although it is difficult to compare production times of method 3 with those of 1 and 2 there is reason to believe that the latter are not as economical as the former in production costs. There is no difficulty in maintaining an output of five overlaps per 7-h day. The resulting accuracy of the test was not less than that of the analytical method. We have not had much experience in using plotters other than the Wild A8 for the production of aerotriangulation by the observation of independent models. We hope that plotters capable of dealing with super-wide-angle photography will soon be fitted with a suitable read-out. An instrument which might lend itself admirably to this purpose is the P.G.2 by Kern of Aarau. This instrument, which can produce surprisingly accurate analogue bridging for height, allows a rapid relative orientation to be performed. Owing to the design of the instrument, however, the coordinates of one of the perspective centres would change with each successive model, and would have to be introduced as a variable value into the tape, but the remainder of the operation could well develop into a rapid method for producing the data for topographic mapping. Another project which interests us is the correction of errors from slightly deformed photography. By analysing the model deformation in a controlled model we hope to be able to arrive at corrections which can be fed automatically into the computing programme at the same time as the observations. The development of "Aerotriangulation by the observation of Independent Models", which we have shortened to A.I.M. for the convenience of our staff in the Directorate, has been sporadic and spread over the years since both of the authors are engaged not so much in research and development as in the day to day production of maps. We have been aware of a climate of opinion which has influenced the development of A.I.M. THOMPSON (1964) mentioned the work of H. G. Fourcade who was working in 1926 to produce an instrument for the express purpose of triangulating in this way. THOMPSON (1959) gave formulae (subsequently improved by SCHUT, 1960) for use in obtaining the relationship of two sets of three dimensional coordinates. Photo~,,ramnTetria 21 (1966) 95-.99
AEROTRIANGULATION BY INDEPENDENT MODELS
99
INGHILLERI (1962--1964) gave an account of his work on this technique using a Stereosimplex Santoni plotter at the Delft meeting, and has reported on further work (INGIatLLERI, 1965). In the early 1950's the I.G.N. (Paris) were using a version of the adjustment of independent model technique. It has been well said that every scientific or technical advance rests on the shoulders of those who went before and the authors are particularly conscious of the truth of this saying in the case of A.I.M. We wish particularly to acknowledge ScHUT's (1960, p.35) equations which have greatly assisted the computational work involved in A.I.M.
REFERENCES INGHItLERI, G., 1964. Some experiments of semi-analytical triangulation. Photogrammetria, 19(7): 273-274. IN6mLLERI, ¢3, 1965. Contributions to the study of semi-analytical triangulation, ltalmapE.I.R.A. Chronicle, 1 2 : 5 7 - 7 2 SCHUT, G. H., 1960. On exact linear equations for the computation of the rotational elements of absolute orientation. Photogrammetria, 17(1): 34-37. THOMPSON, E. H., 1959. A method for the construction of orthogonal matrices. Photogrammetric Record, 3(13): 55-59. THOMPSON, E. H., 1964. Aerial triangulation by independent models. Photogrammetria, 19(7): 262-265. WILLIAMS. V. A. and BRAZIER, H. H., 1964 Aerotriangulation by the observation of independent models. Photogrammetria, 19(7): 275-278. WIt, L~AMS, V. A. and BRAZIER, H. H., 1965, The method of the adjustment of independent models. Photogrammetric Record, 5(26): 123-130.
PhotoL,rammetria 21 (11966) 95 99