Aerial triangulation by independent models

262

Aerial Triangulation by Independent Models by Prof. E. H. T H O M P S O N U n i v e r s i t y College London The subject I h a v e chosen f o r this m e e t i n g is Aerial T r i a n g u l a t i o n by Independent Models. It is a subject t h a t h a s interested me over m a n y y e a r s but it is not one t h a t I t h o u g h t w a s p a r t i c u l a r l y p o p u l a r : I a m g r a t i f i e d to find two other p a p e r s in t h i s s y m p o s i u m on t h i s subject which shows t h a t it h a s possibly a g r e a t e r i n t e r e s t t h a n one would have suspected. I a m interested in the method for two reasons. F i r s t , I w a s b r o u g h t up with it, for I w a s m u c h influenced d u r i n g m y early y e a r s in p h o t o g r a m m e t r y by t h e work of Dr. H. G. Fourcade who developed an i n s t r u m e n t for the e x p r e s s purpose of t r i a n g u l a t i n g in t h i s w a y [1]. Second, I have, in more recent years, been concerned with the development of a precise plotting i n s t r u m e n t t h a t is not capable of the fully a n a l o g o u s method of strip t r i a n g u l a t i o n . My i n s t r u m e n t , a s I have mentioned several times in w r i t t e n papers, is based v e r y m u c h on Dr. F o u r c a d e ' s ideas and I h a v e succeeded in r e t a i n i n g his principle of m a k i n g the i n s t r u m e n t a s a c c u r a t e as possible for relative orientation while allowing the coordinate m e a s u r e s to take care of themselves, so to speak. The problem of aerial t r i a n g u l a t i o n by independent models is t h a t of t r a n s f o r m i n g the coordinates of points m e a s u r e d with respect to a s y s t e m peculiar to a given model to a s y s t e m common to the whole strip. The c h a n g e s of origin a n d scale are relatively e a s y to handle: the rotation between the coordinate s y s t e m s is more difficult to obtain. There are, I think, f o u r w a y s in which this can be done. T h e f i r s t , and m o s t obvious, is to m e a s u r e for the p h o t o g r a p h common to two successive models, its relative orientation tilts by m e a n s of the scales provided and to calculate f r o m these the rotation m a t r i x R _ of this p h o t o g r a p h with respect to the coordinate s y s t e m of the preceding model and R ÷ w i t h respect to the s y s t e m of the succeeding model. The relative rotation between t h e two s y s t e m s is t h e n given by R = R _ RT+. The d i s a d v a n t a g e of this direct method is t h a t we h a v e to rely on tilt scales t h a t a r e not u s u a l l y as a c c u r a t e for the m e a s u r e m e n t of rotations as we require. F u r t h e r m o r e the computation of the rotation m a t r i c e s f r o m the a n g u l a r r e a d i n g s is a w k w a r d on a desk calculating m a c h i n e and there is no plotting i n s t r u m e n t in existence in which these angles can be a u t o m a t i c a l l y recorded. The provision of a recording s y s t e m would be difficult a n d a h e a v y additional expense which could h a r d l y be justified. The second method, adopted by Fourcade, was to m e a s u r e the rotation of the photog r a p h s (in ~ a n d o) b u t not in k) by m e a n s of a c c u r a t e a n g u l a r scales a t t a c h e d to the s c a n n i n g s y s t e m of his i n s t r u m e n t . The scales were designed to m e a s u r e the angles t h a t a pair of c o r r e s p o n d i n g r a y s m a d e with t h e air base and the inclination t h a t the epipolar plane c o n t a i n i n g the r a y s m a d e with some a r b i t r a r i l y chosen reference plane. His ins t r u m e n t did not t r a n s f o r m these bi-polar coordinates into r e c t a n g u l a r coordinates (as does a plotting i n s t r u m e n t ) and r e c t a n g u l a r coordinates could not t h e r e f o r e be m e a s u r e d . A f t e r a p a i r of p h o t o g r a p h s h a d been set i n relative o r i e n t a t i o n the directions to some m a r k e d point on a picture (in f a c t the principal point) were obtained. The rotation of the picture in its own plane (k) w a s m e a s u r e d directly by a g r a d u a t e d scale. T h i s method is a slight i m p r o v e m e n t on the f i r s t b u t difficulties of a u t o m a t i c recording a n d m a n u a l computation still remain. The third method, and historically the n e x t to be used, w a s introduced by the I.G.N. in P a r i s [2, 3] and is, with some modification, possibly the best. It goes a step beyond the Fourcade method by m e a s u r i n g two m a r k s on the pictures and by m a k i n g use of the

[4]

Thompson, Ae~'ial T~iangulation by Independent Models

263

r e c t a n g u l a r coordinate scales t h a t every precise plotter possesses. The rotation matrices R _ and R + a r e computed from measures to a pair of suitably placed artificial m a r k s on the picture common to two models. If I have understood the method correctly, the formulae used to calculate the matrices are approximate, buth there is no need for this and the measures lend themselves to extremely simple rigorous computation. We define t h e rotation of a picture (with respect to a given model system) by the coordinates of two collimating m a r k s (or rdseau intersections) a t equal distances on either side of the principal point, the line joining them being roughly across the strip. We take the untilted coordinates of these two points to be, respectively, (0 y f) and (0 - - y f) where f is the principal distance and y the distance of each point from the principal point. A f t e r a rotation R the coordinates will be (0 y f ) R r and (0 - - y f ) R I respectively; a n d the projection of these two points in the model space a t some chosen value of the projection distance can be observed and will have coordinates given by,

YA

= OAR

y

and

YB

/

za

= QBR

Z.

where ~A and ~B are scale factors. Usually we could take Z A = Z B but this is not necessary. If R , j is the j t h column of R then,

-°aY R*2 + ~.AfR*3

YA ZA

--~BY R.2 + ~Bf R*3 =

YB

and

whence,

R*2

R*I

=

2YQA

YA ZA

~

YA Z.4

-

-

+

2Y~B

YB , ZB

1 2feb

Yn ZB

Since the columns of R are m u t u a l l y perpendicular u n i t vectors, R.1 is the vector product of R.2 and R,3 , t h a t is, 0 R*I

=

9"32

\ --r22

----r32 0

r12

r22 ) ----or 12

R,3

0

where r~i is a typical element of R. Alternatively, R.1 m a y be obtained by noting t h a t every element of a n orthogonal m a t r i x is equal to its cofactor, b u t the computor may find. the vector product the easiest way of g e t t i n g his signs right. Also, m a k i n g use of the orthogonal properties of R, or otherwise,

QA = (XA2 + Y A 2 + ZA2)'/~/(Y2 "~ f2)'h 0 B = (X~2 + yB2 + ZB2),/~/(y2 + [2)'/2

7

[5]

264

Pho~ogrammetria, XIX, No. 7

The rigour of these formulae seems to be advantageous in these days as the data become more and more accurate; and one should not, I think, rely upon the good quality of the flying in order to be able to use approximate formulae. The f o u r t h method is one I proposed in a paper about 1959 in "Photogrammet r i a " [10] where the triangle formed by the airstation and two pass points observed in successive models is used to c a r r y out an absolute orientation of one model with respect to its neighbour and so to obtain R. This method was originally proposed because it used w h a t I thought to be a reasonably simple set of equations for determining the elements of R. T h e s e w e r e subsequently improved in a paper by Mr. Schut [11] ; and I think t h a t from the point of view of observation and computation, the method, using Mr. Schut's equations, is the simplest of all, Nevertheless, on balance, I am of the opinion t h a t the third method mentioned above is the best. It has the minor d i s a d v a n t a g e t h a t a small amount of extra observing is necessary: artificial pass points have to. be observed in addition to the photographic points needed for t r a n s f e r r i n g scale. The computations are extremely simple and it will be noted that, unlike any other method, six elements of any orthogonal m a t r i x are computed directly from the observations. On grounds of accuracy there is reason to suppose the method the best. As Poivilliers has pointed out, the observation to artificial marks, on which the rotation depends, is likely to be more accurate t h a n observation to photographic points; and if the rotation does not depend upon the photographic points (as it does in the fourth method above) discrepancies will appear at the pass points to give valuable i n f o r m a t i o n about the precision and to s t r e n g t h e n the tie. Some experimentation will be required to prove this last hypothesis. These are then the four strictly independent model methods t h a t appear to me to be practicable. There are however several intermediate methods in which some of the computation is eliminated by the use of spirit levels [4, 5], or autocollimators [6], or the somewhat u n s a t i s f a c t o r y method I proposed and introduced into the f i r s t model of my plotting i n s t r u m e n t [7] and which has now been eliminated in the latest model [8]. More recently H. Yzerman [9] has proposed a method which he uses with his plotter, the Kern P.G.2, in which the rotations are computed and applied to the absolute orientations of each model. In all these compromise methods the vertical, and sometimes the scale, are carried t h r o u g h the strip. It is however not possible to r e f e r the plan coordinates to a single system and, although the computations are simple once the vertical has been established, the methods are untidy and, having regard to the more complicated observing procedure in every case, no quicker and probably less accurate than a s t r a i g h t f o r w a r d application of the independent model. The obvious a d v a n t a g e of the independent model method is t h a t it can be used with any plotting instrument: a universal i n s t r u m e n t is not required. In princip!e, triangulation should be more accurate by independent models because, even when carried out in a universal instrument, the absolute orientation elements can remain untouched, as was pointed out by Poivilliers in [2]. It can also be carried out in instruments t h a t are perhaps better able to obtain high accuracies because they are mechanically simpler. My only experience of such a comparison has been between my Model 2 instrument and a Zeiss C 8 Stereoplanigraph in which the results showed no significant difference and it is therefore too early to say whether there is any substance in the above supposition. The disadvantage is t h a t some e x t r a computation is required. This is, I think, more a p p a r e n t than real for the heavy computation of building strips into blocks and adjusting the blocks is unavoidable by any method. Even if automatic digital computers are not available, the formulae now at our disposal for model connexion can be handled on a desk machine. Although it is a question t h a t concerns all methods of aerial triangulation I would like to say something about E a r t h curvature. I was very gratified to see t h a t earth curvature is treated by Mr. Brazier in a rational m a n n e r . i n his paper. Some photogram-

[6]

Thompson, Aerial Triangulation by Independent Models

26~

metrists, perhaps even the majority, t r e a t the effects of earth curvature as an e r r o r when it is nothing of the sort. If we deliberately take two rectangular coordinates X and y 1) and combine these with a third parameter, the height, which is a polar coordinate directed roughly towards the earth's centre, and t r e a t these three as if they w e r e a set of rectangular coordinates in space, it is not surprising t h a t some peculier effects appear looking for all the world like errors. It seems much more satisfactory to me to follow Mr. Brazier and t r e a t the p h o t o g r a m m e t r y as if it were, if not correct, at least correct in principle. Photogrammetric measurement gives you, a p a r t from e r r o r s of measurement, the correct relative positions in space of points. Heights arise in geodetic measurement only because the spirit level gives the surveyor a convenient reference direction: they have no place in p h o t o g r a m m e t r y and merely confuse the issue. By working in true rectangular coordinates on the ground, we avoid the difficulty. To conclude, I would like to give you some results I have obtained using my ins t r u m e n t on a block of two strips of six pictures each, with 6 control points. The results are in planimetry only, because this experiment was done for cadastral survey purposes. The heights were, of course, necessary for absolute orientations, but the checks were in planimetry only, on a g r e a t many points, and enough to make the results significant. With the Hilger and W a t t s stereocomparator we obtained an error of 14 ttm. U s i n g those same diapositives in m y plotting instrument we had 18 ~tm; and in a universal ins t r u m e n t 19~m. They were computed i n the way I have described in "Photogrammet r i a " [10], by f i t t i n g one model to the other in absolute orientation, and the block was adjusted in planimetry by using the method developed by Dr. Fouad Amer, when he was with me at University College London. Between the stereocomparator and the analogue instruments there is not a g r e a t decrease in accuracy and there is certainly an advantage in the sense t h a t you do not need a special instrument. As you know I have been v e r y keen on stereocomparator work, and I am tired of hearing people say t h a t trouble with stereocomparators is t h a t they cannot plot! I must myself now say t h a t the advantage of the analogue instrument is t h a t it can plot. Another advantage, as Mr. Brazier has pointed out, is that the data is much easier to handle for there is much less of it. The most difficult p a r t of the computation, the relative orientation, is done for you by analogue and you can be sure t h a t there is nothing w r o n g with the data up to t h a t stage: the subsequent data are relatively simple. These are certainly advantages for smaller organizations who may" be frightened, as I think they have every r i g h t to be, of handling stereocomparator observations. REFERENCES. [1] Transactions of the Royal Society of South Africa, XIV, pt. 1, p. 93, 1926. [2] Inteqmational Archives for Photogrammet~y, X, pt. 2, 1950. [3] Ibid., XI, pt. 2, 1952. [4] The South African Journal of Photogrammetry, I, 4, May 1962. [5] The Photogrammetrie Record, III, 15, April 1960. [6] International Archives for Photogrammetry, XIII, pt. 4, 1961. [7] The Photogrammetrlc Record, I, 3, April 1964. [8] Ibid., IV, 23, April 1964. [9] Ibid., IV, 21, April 1964. [10] Photogrammetria, XV, 4, 1958-59. [11] Ibid., XVII, 1, 1960-61. 1) Which are not even strictly space coordinates but plane map coordinates containing all the projection deformations.

Photogrammetria, XIX, No. 7

266

Discussion Brandenberger:

A r e t h e s e e r r o r s y o u h a v e q u o t e d s t a n d a r d e r r o r s or root m e a n

square errors?

Thompson: T h e s e a r e s t r i c t l y s p e a k i n g root m e a n s q u a r e e r r o r s , a n d a r e e r r o r s of t h e vector, t h a t is to s a y n o t s e p a r a t e l y in X a n d Y. T h e y a r e root m e a n s q u a r e e r r o r s in t h e s e n s e t h a t t h e y a r e t h e s q u a r e r o o t s o f t h e m e a n s of t h e s u m of t h e s q u a r e s of t h e d i f f e r e n c e s of t h e p h o t o g r a m m e t r i c r e s u l t s a n d t h e r e s u l t s s u p p l i e d to u s f r o m t h e g r o u n d s u r v e y . T h e y a r e n o t s t a n d a r d e r r o r s in t h e s e n s e o f s t a n d a r d d e v i a t i o n s f r o m a mean error. Jerie: P r o f . T h o m p s o n m e n t i o n e d t h a t t h e F r e n c h m e t h o d could be i m p r o v e d by u s i n g p r i c k e d m a r k s f o r t h e t r a n s f e r points. Could t h a t n o t be combined in t h i s m e t h o d a s well? C o u l d h e n o t u s e p r i c k e d p o i n t s f o r t h e tie p o i n t s in h i s m e t h o d a s well, w h i c h should give exactly the same result. Thompson: I f I u n d e r s t o o d t h e F r e n c h m e t h o d correctly, t h e s i m p l i c i t y in t h e c o m p u t a t i o n lies in t h e f a c t t h a t t h e p o i n t s u s e d a r e s y m m e t r i c a l l y s i t u a t e d in t h e model. T h a t m e a n s t h a t p a s s p o i n t s a r e r u l e d o u t f o r t h i s p u r p o s e . I do a g r e e t h a t , if one is p r e p a r e d to c o m p l i c a t e t h e a r i t h m e t i c , ( t h e r e is n o t h i n g in t h i s if a n a u t o m a t i c comp u t e r is u s e d ) a n d if t h e p o i n t s were to be p r i c k e d on t h e c e n t r a l p h o t o g r a p h of a g r o u p of t h r e e , t h e n t h e p a s s p o i n t s could be u s e d . I w o u l d like to s u g g e s t t h a t t h e s e m e t h o d s o u g h t to be divided in two g r o u p s : t h o s e t h a t a r e c a p a b l e o f b e i n g done on a desk c a l c u l a t o r a n d t h o s e t h a t r e q u i r e a h i g h speed c o m p u t e r . O n e of t h e a d v a n t a g e s of t h e i n d e p e n d e n t m o d e l m e t h o d s is t h a t a s m a l l o r g a n i z a t i o n t h a t h a s a p l o t t i n g m a c h i n e b u t h a s no a c c e s s to a c o m p u t e r , c a n u s e t h e m . de Masson d'Autume: Bien que les q u e s t i o n s h i s t o r i q u e s soient en g~n~ral de p e u d'int~r~t, j ' a i relev~ u n e p e t i t e e r r e u r d a n s la c o m m u n i c a t i o n d u P r o f . T h o m p s o n . Q u a n d il p a r l e de la m ~ t h o d e ,,par modules i n d ~ p e n d a n t s " il f a i t a l l u s i o n ~ u n e m ~ t h o d e qui a u r a i t ~t~ publi~e p a r Poivilliers d a n s les C o m p t e s - R e n d u s d u 8 m e C o n g r ~ s , 1952. E n f a i r si l'id~e p r e m i e r e de la t r i a n g u l a t i o n p a r modules i n d ~ p e n d a n t s telle qu'elle e s t p r a t i q u ~ e ~ I ' I G N r e m o n t e b i e n ~ M. Poivilliers, cette m~thode, dite , , c h e m i n e m e n t a l t i t u d e c o n s t a n t e " n ' a en f a i t j a m a i s ~t~ raise en p r a t i q u e . L a m ~ t h o d e qui a ~t~ ~labor~e p a r la s u i t e ~ I ' I G N , et en p a r t i c u l i e r l'id~e de m a i n t e n i r la b a s e c o n s t a n t e et de s u p p r i m e r l ' i n v e r s i o n de la b a s e , ne d o i v e n t p a s g r a n d - c h o s e ~ M. Poivilliers. D , a u t r e p a r t , n o u s a v o n s utilis~ ~ I ' I G N d e n x m ~ t h o d e s d ' e n c h a ~ n e m e n t des m o d u l e s i n d ~ p e n d a n t s : la p r e m i e r e qui u t i l i s e les p o i n t s de c a n e v a s c.O.d, des p o i n t s a u sol, et u n e d e u x i ~ m e m ~ t h o d e qui u t i l i s e n o n p a s des p o i n t s r~els a u sol m a i s d e s p o i n t s f i c t i f s q u i s o n t p i q u e s s u r le n ~ g a t i f . Ces d e u x m ~ t h o d e s o n t l e u r s a v a n t a g e s et l e u r s i n c o n v ~ n i e n t s . D a n s le c a s p a r t i c u l i e r off les cliches s o n t tr~s m a u v a i s il v a u t m i e u x p i q u e r des p o i n t s s u r le n ~ g a t i f q u e d ' u t i l i s e r des d~tails n a t u r e l s qui p e u v e n t ~tre p l u s ou m o i n s nets. D u p o i n t de v u e t h ~ o r i q u e cela n e c h a n g e p a s g r a n d - c h o s e a u calcul. Thompson: E s t - c e que j ' a i bien c o m p r i s que la m ~ t h o d e expos~e d a n s les A r c h i v e s ~ t a i t u n e m ~ t h o d e a p p r o x i m a t i v e ? E s t - c e que c ' e s t u n e m ~ t h o d e d o n t les f o r m u l e s s o n t au correctes premier ordre pros? de Masson d'Autume: L a m ~ t h o d e d o n t il a ~t~ r e n d u c o m p t e a u c o n g r ~ s de W a s h i n g t o n e s t u n e m ~ t h o d e a p p r o x i m a t i v e , m a i s la m ~ t h o d e qui a ~t~ publi~e ~ Foccasion

[8]

Discussion on the paper of Thompson

267

du congr~s de Londres est u n e m~thode rigoureuse, f a i s a n t appel a u x m a t r i c e s - r o t a t i o n . C'est ~ p a r t i r de 1959 que n o u s avons commenc4 ~ utiliser la m~thode d ' e n c h a i n e m e n t rigoureuse, bas~e s u r la consideration des m a t r i c e s - r o t a t i o n , et cette m~thode est m~me plus compliqu~e que celle ~ laquelle vous avez fair allusion, p u i s q u ' o n proc~de ~ u n e compensation i n t e r n e de la bande et qu'on d~forme chaque module de mani~re ~t am~liorer le raccord e n t r e deux modules cons~cutifs.

Tewinkel: First, I wish to agree with Prof. T h o m p s o n in t h a t e a r t h c u r v a t u r e is theoretically t a k e n care of exactly t h r o u g h the use of proper geometric t r a n s f o r m a t i o n . However, some small p r i v a t e f i r m s find it practical to apply e a r t h c u r v a t u r e like a lens distortion. T h i s u s u a l l y avoids one or m o r e t r i p s to t h e electronic c o m p u t e r w i t h o u t s i g n i f i c a n t l y d a m a g i n g the p h o t o g r a m m e t r i c solution. Thompson: If you are plotting a single model and e a r t h c u r v a t u r e is s i g n i f i c a n t you m u s t t a k e account of it and t r e a t it as a n error, because contours a r e required and t h e y are t h e intersections of equipotential s u r f a c e s with the t o p o g r a p h y . If you intersect the t o p o g r a p h y with planes of c o n s t a n t Z, which is w h a t a p h o t o g r a m m e t r i c a n a l o g u e i n s t r u m e n t will do if you leave it alone, you will get, p a r t i c u l a r l y w i t h s u p e r wide angle p h o t o g r a p h y , a s i g n i f i c a n t l y w r o n g answer. T h e r e f o r e you m u s t correct f o r it u n d e r such circumstances. I w a s t a l k i n g purely of aerial t r i a n g u l a t i o n a n d not of plotting. Schut: I do not see w h y the correction for e a r t h c u r v a t u r e o u g h t to involve the use of geocentric coordinates, geographic coordinates a n d m a p projection formulae. One can c o n s t r u c t a three dimensional r e c t a n g u l a r coordinate s y s t e m f r o m horizontal m a p coordinates a n d t e r r a i n heights. Then, all t h a t is n e c e s s a r y in the case of an analytical t r i a n g u l a t i o n is to correct t h e p h o t o g r a p h coordinates for e a r t h c u r v a t u r e . W i t h app r o x i m a t e l y vertical p h o t o g r a p h y , this can be done by a radial correction. In the case of a n aerial t r i a n g u l a t i o n w i t h a plotting i n s t r u m e n t one can give the t r i a n g u l a t e d s t r i p proper c u r v a t u r e corrections in the l a t e r a l direction a n d in t h e longitudinal direction. In the tongitidunal direction, with a strip of a n y l e n g t h one a l w a y s h a s to apply a longitudinal correction for h e i g h t deformation a n d in t h a t case one can j u s t apply one empirical longitudinal c u r v a t u r e correction for e a r t h c u r v a t u r e a n d s t r i p deformation together. In t h i s way, the correction of e a r t h c u r v a t u r e , is v e r y simple. Thompson: I a m n o t quite s u r e I u n d e r s t a n d Mr. S c h u t ' s point. It is a l w a y s necess a r y to apply the c u r v a t u r e correction in the longitudinal direction, isn't it? Schut: I f one h a s a s t r i p of a n y l e n g t h one u s u a l l y f i n d s t h a t there is h e i g h t distortion a n d one h a s to a p p l y a longitudinal c u r v a t u r e correction. Thompson: Of course, b u t I think it is m u c h better in principle to s e p a r a t e e r r o r s which are e r r o r s f r o m e f f e c t s which are not errors a t all. It is s i m p l y t h a t it is m e s s y to do it the other way. It seems to me t h a t you are i n t r o d u c i n g difficulties t h a t j u s t do not exist. I t is m u c h easier to take y o u r r e c t a n g u l a r coordinates a n d your h e i g h t s a s Mr. Brazier does and compute f r o m these geocentric coordinates. You a r e t h e n not int r o d u c i n g e r r o r s into s o m e t h i n g correct b u t a r e m e r e l y e x p r e s s i n g t h e d a t a in a d i f f e r e n t way. W h e n you modify the p h o t o g r a m m e t r i c m e a s u r e s you a r e i n t r o d u c i n g e r r o r s into s o m e t h i n g t h a t does n o t h a v e them. Schut: One can t a k e care of all e r r o r s in longitudinal direction a n d of t h e e a r t h c u r v a t u r e in one step in the a d j u s t m e n t . I do not see a n y t h i n g m e s s y in this and in t h i s w a y the l e n g t h y computation via geocentric and geographic coordinates i s a v o i d e d . I 7 *"

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McNair: I believe t h a t it is only f a i r to s a y t h a t in w o r k i n g with geocentric coord i n a t e s one is likely to h a v e v e r y large n u m b e r s . This m a y require a l a r g e r capacity c o m p u t i n g m a c h i n e a n d c o m p u t i n g p r o g r a m m e t h a n would be required u s i n g a plane s u r f a c e a n d m a k i n g corrections f o r e a r t h c u r v a t u r e . I f one h a s t h e capacity in his calculator it is m u c h easier to use geocentric coordinates directly, b u t if the strip is s h o r t or i f one h a s a limited capacity m a c h i n e it is easier to u s e plane coordinates and t h e n m a k e corrections f o r e a r t h c u r v a t u r e if this is necessitated by h i g h p h o t o g r a p h y or a l o n g strip. Thompson: I h a v e only used the expression geocentric coordinates, because Mr. B r a z i e r describes in detail in his p a p e r how he used them, but of course this is not basically w h a t I m e a n t to s a y which w a s t h a t you m u s t use r e c t a n g u l a r coordinates a n d if you choose r e c t a n g u l a r coordinates with the origin a t the centre of the e a r t h you m a y do so. Brazier: I t h i n k I o u g h t to s a y s o m e t h i n g about this, because w h e n you h a v e a f a i r l y large c a p a c i t y computer (in f a c t o u r s is the one we u s e for geodetic work), one does n o t need to t r a n s f e r the origin to the t a n g e n t i a l p l a n e ; we u s u a l l y choose a l o n g i t u d i n a l origin t h a t wilt p a s s f a i r l y close to the a r e a t h a t we are dealing w i t h so t h a t we do n o t g e t a large coordinate. I r a t h e r agree w i t h Prof. T h o m p s o n t h a t all s y s t e m a t i c e r r o r s t h a t one knows about, should be removed, a n d w h e n you have done y o u r a d j u s t m e n t onto three-dimensional r e c t a n g u l a r coordinates you have a n i m m e d i a t e e s t i m a t e of t h e a m o u n t of e r r o r which y o u r p h o t o g r a m m e t r y h a s produced. Now either t h i s is tolerable a t a certain scale of m a p p i n g or it is not. I f it is, t h e n you directly proceed to p l o t t i n g ; o u r experience is t h a t one can g e n e r a l l y go to about 8 to 10 models w i t h o u t i n t r o d u c i n g a s i g n i f i c a n t error (I a m a s s u m i n g t h a t you are p l o t t i n g a t a scale n o t more t h a n 5 t i m e s t h a t of y o u r p h o t o g r a p h y ) . I f y o u r s t r i p is longer t h a n t h a t you h a v e to adopt empirical f o r m u l a e a n d you can t h e n go into E and N and h, u s i n g y o u r s t r i p coordinates z, y a n d z of t h e m a c h i n e as p a r a m e t e r s for t h a t a d j u s t m e n t . - I t h i n k t h i s is the logical w a y to do it. I: a m not s a y i n g t h a t Mr. Schut will g e t a n y d i f f e r e n t a n s w e r s , b u t I t h i n k t h a t w h e n you are c o m p u t i n g you should compute in a logical fashion. King: I a m n o t clear on one t h i n g here, w h e t h e r Prof. T h o m p s o n is u s i n g g r o u n d control in h i s a d j u s t m e n t , or w h e t h e r he is t r y i n g to g e t a set of strip coordinates as you would g e t f r o m t h e u n i v e r s a l plotter a n d t h e n a d j u s t them. I f he is a c t u a l l y going to u s e the g r o u n d control in the model points, how does he do t h a t ? Thompson: T h e g r o u n d control is n o t used at all at t h e stage of observing. O n e c a r r i e s out a relative orientation followed by a m e a s u r e m e n t of coordinates with respect to t h e model s y s t e m which is of course d i f f e r e n t in every model. In t h e n e x t s t a g e the models a r e joined t o g e t h e r to f o r m a strip. Now this can be done in one of two ways. If one h a s e n o u g h i n f o r m a t i o n on the f i r s t model to orient it absolutely, and scale it, ±hen it m i g h t be a n a d v a n t a g e to correct t h e model so as to obtain coordinates directly i n the geodetic s y s t e m , but if t h e r e is not enough i n f o r m a t i o n on a n y one of the models t h e n t h e y are joined t o g e t h e r on w h a t is now a n a r b i t r a r y system. The g r o u n d control is t h e n introduced to give the absolute orientation of each s t r i p a n d this is t h e n followed by a block a d j u s t m e n t u s i n g t h e method developed by Dr. A m e r at U n i v e r s i t y College. Roelofs: I would like to a d d one more point w i t h r e g a r d to i n d e p e n d e n t models. In t h e b e g i n n i n g of his lecture Prof. T h o m p s o n m e n t i o n e d 3 o r 4 m e t h o d s Of o b s e r v i n g independent models, by r e a d i n g the scales f o r rotations, or u s i n g the coordinates of t h e

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c a m e r a station and o f some points in the model. Now, Prof. T h o m p s o n mentioned the d i s a d v a n t a g e of the f o r m e r method, s a y i n g t h a t the s c a l e s for r e a d i n g t h e rotation are g e n e r a l l y not a c c u r a t e enough, depending on t h e i n s t r u m e n t of course. T h e r e is one more d i s a d v a n t a g e , I think. W h e n a n a l y s i n g the pilot models on the O E E P E we discovered t h a t the r e a d i n g s of t h e rotation scales are not a l w a y s r e p r e s e n t a t i v e of the rotation, depending on t h e i n s t r u m e n t a n d on its state of a d j u s t m e n t . In o t h e r words, the r e a d i n g s on the rotation scales a r e not a l w a y s r e p r e s e n t a t i v e for w h a t is h a p p e n i n g in the model. So t h a t is one more d i s a d v a n t a g e of t h i s f i r s t method.

Thompson: I e n t i r e l y a g r e e with Prof. Roelofs here. In the m a n u f a c t u r e of m y own i n s t r u m e n t , in order to reduce the cost we have endeavoured to m a k e the rotation m o v e m e n t s of t h e projectors s u f f i c i e n t l y a c c u r a t e a s m i c r o m e t e r s to enable one to apply small c h a n g e s w i t h some degree of certainty. T h e y are certainly n o t good enough to give absolute tilt r e a d i n g s w i t h the desired accuracy. Weightman: If in f a c t t h e observations are equivalent to theodolite observations on one face, could you p e r h a p s i n t e r c h a n g e t h e p h o t o g r a p h s a n d reobserve? You know almost exactly the s e t t i n g s t h a t you need. A quick reobservation would give you t h e n e c e s s a r y c h a n g e to allow for the "collimation of the i n s t r u m e n t " , as it were. Thompson: I t h i n k the i n t e r c h a n g e is bound to eliminate some of the errors. One could probably devise a drill by which t h i s is done, I h a v e a f e e l i n g t h a t in order to eliminate the e r r o r it is not only n e c e s s a r y to i n t e r c h a n g e p h o t o g r a p h s between projectors, b u t also to use t h e two halves of the s a m e projector. B u t even if t h i s were successful w h a t is the point? It a d d s e x t r a observations t h a t can be avoided by not u s i n g t h e scales. Pryor: My question p e r t a i n s to the discovery of e r r o r s e x i s t i n g because of i m a g e d e f o r m a t i o n in the p h o t o g r a p h y . Maybe error exists because the stereoscopic model is of s u c h a c h a r a c t e r t h a t the p a r a l l a x cannot be removed. I f you h a v e p h o t o g r a p h y in a S t e r e o p l a n i g r a p h for example, it would be obvious if i m a g e d e f o r m a t i o n s were m a k i n g removal of p a r a l l a x impossible. Yet, if I u n d e r s t a n d correctly, it would not be possible to discover lack of image correlation in a stereoscopic model being formed by use of p h o t o g r a p h y c o n t a i n i n g i m a g e deformation as the coordinates a r e m e a s u r e d separately. Would the s e p a r a t e e r r o r s due m a y b e to m o v e m e n t of emulsion, to f i l m s h r i n k a g e , to diff e r e n t i a l c h a n g e s in scale of t h e model, a n d so forth, be discovered in this m a t h e m a t i c a l method? Thompson: I a m a f r a i d t h a t the method h a s been misunderstood, because as f a r as relative orientation is concerned and all t h e checks t h a t arise f r o m it, such as e r r o r s due to the m o v e m e n t of t h e film etc., there is no change f r o m the B i l d a n s c h l u s s method. A r~lative orientation is carried out and the model can be examined. It is only f r o m this s t a g e o n w a r d s t h a t it becomes a computational method. In this respect it is a h a l f w a y house between the s t e r e o c o m p a r a t o r m e t h o d s where only r e c t a n g u l a r coordinates are m e a s u r e d , a n d the completely n o n - c o m p u t a t i o n a l methods where in f a c t t h e r e c t a n g u l a r coordinates of a strip a r e obtained directly a f t e r the relative orientation of the new photograph. AcI~ermann: Prof. Thompson, r e g a r d i n g the test-block you r e f e r r e d to I u n d e r s t a n d t h a t you m e a s u r e d the models independently. F r o m these, s t r i p s were computed a n d a f t e r t h a t a b l o c k - a d j u s t m e n t procedure, w a s applied, which a g a i n cut the s t r i p s u p into i n d e p e n d e n t models. W h a t is y o u r opinion on the possibility of o m i t t i n g the strip

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f o r m a t i o n completely, a n d g o i n g directly into the block a d j u s t m e n t with independent models ?

Thompson: T h i s is a point which I h a v e raised in m y p a p e r to Commission III in r a t h e r more g e n e r a l terms. In all t r i a n g u l a t i o n , w h e t h e r geodetic o1" aerial, the comp u t a t i o n is divided into two h a l v e s for r e a s o n s which a r e p u r e l y m a t h e m a t i c a l . T h a t is to say, t h e r e is f i r s t of all a p r e l i m i n a r y computation a n d secondly there is a so called a d j u s t m e n t . Now w h y is this division m a d e ? It is s i m p l y because the a d j u s t m e n t is not a practical proposition a t all u n l e s s it is done with the help of linear equations. Therefore you m u s t g e t to a n a p p r o x i m a t e solution before you can s t a r t a p p l y i n g a n y methods of a d j u s t m e n t , because it would be quite impractical to use t h e non-linear equations at t h e final stage. So the r e q u i r e m e n t is t h a t y o u r p r e l i m i n a r y c o m p u t a t i o n s get somewhere n e a r the r i g h t a n s w e r . To a n s w e r Dr. A c k e r m a n n ' s question, it entirely depends on the q u a l i t y of t h e flying. If the f l y i n g is so good t h a t t h e models join t o g e t h e r to a f i r s t order accuracy, t h e n you could do exactly w h a t he s u g g e s t s . The problem is do t h e y ? I f t h e y do not, t h e n you m u s t do t h i s p r e l i m i n a r y build-up s i m p l y in order to get rid of the n o n l i n e a r p a r t of the work before you s t a r t on the l i n e a r p a r t of the a d j u s t m e n t . de Masson d ' A u t u m e : Le point de vue du P r o f e s s e u r T h o m p s o n qui consiste ~ comm e n c e r le t r a v a i l p a r la connection de d e u x modules c o n t i g u s a une a u t r e raison que la n~cessit4 de lin4ariser les ~quations (ce qui exige la c o n n a i s s a n c e d'une solution approch~e): c'est la ngcessit$ de pouvoir d~tecter les e r r e u r s et ceci doit se f a i r e p a r des calculs p r o g r e s s i f s . C a r si l'on commence le catcul d ' a j u s t e m e n t s a n s avoir dlimin~ les e r r e u r s on pout ~tre certain d'avoir ~ recommencer u n g r a n d hombre de lois a v a n t d'obtenir des r 4 s u l t a t s s a t i s f a i s a n t s , du fair de la presence d ' e r r e u r s q u i n ' a v a i e n t p a s dt~ ddtect~es. Thompson:

J e suis compl~tement d'accord avec vous.

de Masson d ' A u t u m e : E n ce qui concerne la m4thode qui consiste ~ m e s u r e r les r o t a t i o n s d ' u n projecteur pour obtenir la connection des modules, il y a u n a u t r e inconvdnient qui n o u s y a f a i t renoncer, c'est l'impossibilit~ d'obtenir l ' e n r e g i s t r e m e n t autom a t i q u e d ' a n g l e s dorm,s. On p e u t e n r e g i s t r e r a u t o m a t i q u e m e n t des coordonn4es s u r la p l u p a r t des a p p a r e i l s de r e s t i t u t i o n modernes, m a i s on ne p e u t pas, avec les a p p a r e i l s dont nous disposons, e n r e g i s t r e r a u t o m a t i q u e m e n t les r o t a t i o n s a n g u l a i r e s des project e u r s . C'est la raison qui n o u s a f a i t renoncer ~ cette m~thode. Pq,octor: I simply w a n t to elaborate f u r t h e r on Prof. T h o m p s o n ' s a n s w e r to Dr. A c k e r m a n n in relation to the f o r m a t i o n of strips. I a m r e f e r r i n g to the Ordnance S u r v e y technique, which is based on entirely analytical work, b u t I t h i n k at t h i s s t a g e the two m e t h o d s a r e similar, In m y p a p e r in the P h o t o g r a m m e t r i c Record in April 1962, I did s a y t h a t w h e n we h a d introduced a n entirely analytical block a d j u s t m e n t , it w a s no longer n e c e s s a r y to p e r f o r m t h e strip a d j u s t m e n t s . Of course one h a s to f o r m the block before one a d j u s t s it. It is n e c e s s a r y to f o r m the s t r i p s a n d t h e n build the s t r i p s t o g e t h e r into a block which you can a d j u s t onto y o u r control. Since t h e n we h a v e changed o u r m~nds. We h a v e f o u n d t h a t it is in f a c t economical to continue with our strip a d j u s t m e n t before we go into the block a d j u s t m e n t . We still take out the c u r v a t u r e of the s t r i p because it reduces the n u m b e r of iterations t h a t are required in the s u b s e q u e n t block adjustment. In t h a t p a p e r I also pointed out t h a t where a block a d j u s t m e n t h a d h a d to be halted for the reobservation o f two or three plan controls, m o s t observations could be verified d u r i n g the c o m p u t i n g procedure, b u t t h a t the identification of g r o u n d control w a s almost [12]

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u n c h e c k a b t e u n t i l t h e block a d j u s t m e n t . N o w t h a t t h e s t r i p a d j u s t m e n t h a s been int r o d u c e d , r e s i d u a l s a t c o n t r o l s s h o u l d be s m a l l b e f o r e t h e block a d j u s t m e n t is s t a r t e d a n d l a r g e r e s i d u a l s c a n be i n v e s t i g a t e d .

Schermerhorn: I e x p e c t t h i s s u b j e c t will be r a i s e d a g a i n w h e n we s t a r t t h e disc u s s i o n a b o u t m e t h o d s of block a d j u s t m e n t . Brandenberger: I h a v e a n o t h e r q u e s t i o n to P r o f . T h o m p s o n . Did you a t t r i b u t e t h e s a m e w e i g h t to all y o u r o b s e r v a t i o n s or a r e y o u c o n s i d e r i n g i n t r o d u c i n g d i f f e r e n t w e i g h t s ? A second q u e s t i o n , did y o u or a r e y o u c o n s i d e r i n g o n l y t h e a d j u s t m e n t of n e w p o i n t s or a r e y o u e v e n t u a l l y c o n s i d e r i n g t h e a d j u s t m e n t of o r i e n t a t i o n e l e m e n t s ? W e m a d e a t e s t a t Ohio S t a t e U n i v e r s i t y a n d we f o u n d o u t t h a t if we a d j u s t t h e o r i e n t a t i o n e l e m e n t s a n d i n t r o d u c e t h e s e v a l u e s into a second o r d e r p l o t t e r w h i c h h a s dials, we c a n s a v e a b o u t 80% of t h e t i m e in s e t t i n g u p e a c h i n d i v i d u a l model f o r p l o t t i n g p u r p o s e s . I t h i n k t h i s is a n i t e m w h i c h is v e r y o f t e n f o r g o t t e n in a d j u s t i n g a e r i a l t r i a n g u l a t i o n . Thompson:

I a m n o t q u i t e s u r e t h a t I q u i t e follow you, Dr. B r a n d e n b e r g e r .

Brandenberger: M y q u e s t i o n w a s w h e t h e r you a d j u s t s i m p l y p o i n t s , n e w points, or w h e t h e r you also i n c i d e n t a l l y a d j u s t o r i e n t a t i o n e l e m e n t s s u c h a s l a t e r a l a n d longit u d i n a l tilt, s w i n g etc.? Thompson: I c e r t a i n l y do n o t do t h a t . I p u t m y m o n e y on t h e r e l a t i v e o r i e n t a t i o n e l e m e n t s , a s t h e y come o u t of t h e plotter. I do n o t k n o w w h e t h e r y o u m e n t i o n e d a second o r d e r p l o t t e r d e l i b e r a t e l y or w h e t h e r y o u m e r e l y m e a n t a n o n - u n i v e r s a l plotter. A f t e r all t h e r e is a d i f f e r e n c e . I r e g a r d m y i n s t r u m e n t a s b e i n g a s a c c u r a t e a s a n y u n i v e r s a l i n s t r u m e n t a n d t h e r e a r e o t h e r n o n - u n i v e r s a l i n s t r u m e n t s w h i c h I r e g a r d in t h e s a m e c a t a g o r y . T h e r e f o r e , a s f a r a s r e l a t i v e o r i e n t a t i o n is concerned, I do n o t consider t h a t it is a n y w o r s e t h a n a r e l a t i v e o r i e n t a t i o n done in a n y p l o t t i n g m a c h i n e . B u t of course in a second o r d e r i n s t r u m e n t w h e r e t h e r e l a t i v e o r i e n t a t i o n s c a n be r e g a r d e d as b e i n g s e c o n d - r a t e t h e r e m i g h t be some p u r p o s e in a l l o w i n g t h e s e e l e m e n t s to r e m a i n u n k n o w n a n d to be d e t e r m i n e d b y t h e block a d j u s t m e n t . B u t I c e r t a i n l y did n o t do t h i s in t h e e x p e r i m e n t u n d e r d i s c u s s i o n . T h e m o d e l s w e r e o b s e r v e d a n d t h e c o o r d i n a t e s t a k e n off, a f t e r w h i c h t h e o n l y m o d i f i c a t i o n w a s a c h a n g e in t h e i r scale, o r i e n t a t i o n a n d precision. Schermerhorn: A t t h e L o n d o n C o n g r e s s I m a d e a n e f f o r t to i n t r o d u c e m o r e r e a s o n a b l e t e r m s t h a n f i r s t a n d second o r d e r i n s t r u m e n t s , w h i c h a r e m i s l e a d i n g . D e s i g n e r s s u c h a s T h o m p s o n n o w s a y " m y p l o t t e r is j u s t as good", a n d he p r o v e s this. W h y n o t r e f e r to u n i v e r s a l p l o t t e r s , p r e c i s i o n p l o t t e r s a n d t o p o g r a p h i c p l o t t e r s . T h e n you h a v e t h r e e logical c l a s s e s . T h e T h o m p s o n - W a t t s , t h e A8, t h e S t e r e o s i m p l e x 3 a n d t h e S t e r e o m e t r o g r a p h a r e all p r e c i s i o n p l o t t e r s o r n o n - u n i v e r s a l i n s t r u m e n t s . A t t h e m o m e n t I d i f f e r w i t h M o r r i s T h o m p s o n a b o u t t h e title o f C h a p t e r 14, on t h i s s u b j e c t in t h e t h i r d edition of t h e A m e r i c a n M a n u a l o f P h o t o g r a m m e t r y . H e p r o p o s e s to call all i n s t r u m e n t s t r e a t e d in t h a t c h a p t e r u n i v e r s a l p l o t t e r s , w h i c h is also incorrect. I h a v e a q u e s t i o n c o n c e r n i n g t h o s e check p o i n t s w h i c h you u s e d w h e r e you f o u n d 14 ~m root m e a n s q u a r e e r r o r . W e r e t h e y s i g n a l i s e d p o i n t s ? Thompson:

Yes, all t h e s e p o i n t s w e r e m a r k e d on t h e g r o u n d a n d t h e y were v e r y

well m a r k e d .

Schermerhorn:

With high precision height control?

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Photogrammetria, XIX, No. 7

272

Thompson:

I h a d n o t h i n g to do w i t h t h a t !

Schermerhorn:

Otherwise you would have found more!

Thompson: T h i s e x p e r i m e n t w a s done in c o n j u n c t i o n w i t h t h e S u r v e y o r - G e n e r a l of S o u t h e r n R h o d e s i a f o r a c a d a s t r a l e x p e r i m e n t a n d P r o f . S c h e r m e r h o r n h a s a l r e a d y h e a r d s o m e o f t h e r e s u l t s , in f a c t t h e 14 ~ m r e s u l t s w a s g i v e n l a s t y e a r . T h e e x p e r i m e n t w a s done w i t h t w o s e t s o f p h o t o g r a p h s : t h e f i r s t b e i n g a s m a l l h i g h level s e t t a k e n f r o m 7500 ft. g i v i n g u s a scale of 1 : 15,000, t h e second s e t b e i n g a t h a l f t h i s a l t i t u d e , r e q u i r i n g 51 p h o t o g r a p h s to cover t h e s a m e a r e a . W e h a v e n o t h a d t h e e n e r g y to do t h i s l a t t e r in a n y a n a l o g u e i n s t r u m e n t , b u t it h a s b e e n done in a s t e r e o c o m p a r a t o r . T h e r e s u l t s w e r e a p p r o x i m a t e l y twice as b a d as t h e 14 ~m, in f a c t r a t h e r less t h a n twice a s bad, n a m e l y a b o u t 21 ~tm f o r t h e 21 model block, b u t w h e n t h i s is divided b y 2 in o r d e r to g e t t h e g r o u n d e r r o r , y o u g e t a s l i g h t g a i n n a m e l y 10 ~ m i n s t e a d of 14 ~tm, b u t w i t h t h e e x p e n d i t u r e of f o u r t i m e s a s m u c h work. I a m n o t s u r e t h a t t h i s is w o r t h it. Schermerhwrn: Do you still believe t h a t it n e e d s m o r e c o u r a g e to m e a s u r e i n t h e a n a l o g u e m a c h i n e t h a n in t h e s t e r e o c o m p a r a t o r ? Thompson: No, I did n o t m e a n t h a t . It is j u s t n a t u r a l laziness. It w a s p r i m a r i l y a s t e r e o c o m p a r a t o r e x p e r i m e n t a n d it w a s n o t o r i g i n a l l y i n t e n d e d to be a n a n a l o g u e i n s t r u m e n t a l t e s t . T h e r e m a y be a little m o r e o b s e r v i n g w i t h t h e a n a l o g u e i n s t r u m e n t b u t t h e d i f f e r e n c e is negligible.

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