Horizontal aerotriangulation by independent models using horizon camera photography and B-8

Photogrammetria - Elsevier Publishing Company, Amsterdam - Printed in The Netherlands

H O R I Z O N T A L 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 USING H O R I Z O N C A M E R A P H O T O G R A P H Y AND B-8 * EDWARD M. MIKHAIL1 Canadian .4ero Service Limited, Ottawa, Ont. (Canada)

(Received August 30, 1966) (Resubmitted May 20, 1968)

SUMMARY A method for photogrammetric extension of horizontal control for small scale super-wide angle photography is presented. In a slightly modified B-8, independent models are set up and levelled using tip and tilt angles derived from horizon pictures exposed simultaneously with RC-9 vertical photography. Plane coordinates of tie points and available horizontal control points are measured on a coordinatograph for each model independently. Continuous strips are then formed by numerical connection of successive models, and a study of their behaviour is performed using analytical adjustment of single strips. Finally, comparative studies and test results are given for horizontal block adjustment by strips, by segments of strips, and by small sections.

INTRODUCTION During the "Symposium on Aerial Triangulation" held at the International Training Center (I.T.C.) in Delft, August 24-29, 1964, three papers dealing with "aerial triangulation with independent models" were presented. In the first paper THOMPSON (1964) gave an excellent account of the history of the development of this method and its variations, as well as his own contributions regarding applications on the Thompson-Watts plotter. INCHILLERI (1964) gave an account of the method as applied to the Stereosimplex Santoni Model III instrument, and WILLIAMS and BRAZIER (1964) as applied to the Wild A-8. All these methods have at least one common factor: they involve aerotriangulation in three dimensions. The present method, on the other hand, is concerned only with horizontal aerotriangulation. * Paper presented at the International Symposium on Spatial Aerotriangulation, February 28March 4, 1966, University of Illinois, Urbana, Ill. (U.S.A.). 1 Present address School of Civil Engineering, Purdue University, Lafayette, Ind. (U.S.A.). Photogrammetria, 23 (1968) 149-161

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v:. M. MIKHAIL

In the fall of 1961 Canadian Aero Service was awarded a contract for mapping some 28,000 sq. miles in Nigeria at a scale of 1 : 50,000. ZARZYCKI(1963a, b, c, 1964) gave a detailed account of a new mapping system devised for the project which employed super-wide angle photography, horizon photography, modified B-8 plotters, and a combination of other airborne auxiliary equipment. For this project, additional horizontal control was established photogrammetrically using stereo-template laydown. However, it was found that template laydowns for large areas proved to be somewhat slow and uneconomical. Therefore, when Canadian Aero was awarded another mapping project of some 60,000 sq. miles in the winter of 1964, means were sought to develop a more efficient and economical system of horizontal aerotriangulation. It was then decided to investigate a method of triangulation with independent models.

OUTLINE OF THE M E T H O D

Before presenting the details of the method, it is worthwhile to give first an outline and indicate briefly what is meant by aerotriangulation by independent models. On one hand, analytical aerotriangulation methods are based on comparators as instruments for basic measurement and analogue methods make use of universal plotters for fully establishing strips. On the other hand, the methods of aerotriangulation by independent models utilize simple instruments capable of performing relative orientation of single models and leave the task of connecting models and the final adjustment to electronic computers. Therefore these methods may be referred to as semi-analytical methods. The basic operations of the method under consideration consist of: the relative orientation and levelling of separate models; the connection of successive models to form strips; and the final adjustment of strips and/or blocks. Since the method concerns itself with horizontal aerotriangulation, it is necessary that each independent model be levelled after relative orientation. This is readily performed by using horizon photography which is taken simultaneously with vertical photography and forms an integral part of the mapping system.

PHOTOGRAMMETRIC OPERATIONS

As a semi-analytical procedure, part of the steps of carrying out this method involves photogrammetric and instrumental operations. These include: data acquisition from horizon pictures; model set-ups on the B-8; and measurement of model coordinates. The first two operations are fully explained by ZARZYCKI (1963a, b, c, 1964) and therefore only a brief description is given here. The horizon camera photographs the horizon in four directions from which the relative tip and tilt angles for each aerial photograph can be determined. From two terPhotogrammetria, 23 (1968) 149-161

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restrially controlled models at the beginning and end of each strip, the absolute tip and tilt angles for each vertical photograph can be computed. Using these angles, each individual model can be set up, relatively oriented and levelled on a B-8 slightly modified to allow for the direct introduction of the tip and tilt angles. Once a model is established and levelled, the next step is to obtain plane coordinates for the pass-points at the regular six positions, the cross-pass-points between strips and control points wherever available. Since the B-8 does not yield X- and Y-model coordinates, one of two means may be adopted: either the instrument itself (B-8) is fitted with a coordinate recorder; or the points are plotted on sheets of stable material and then their coordinates read off the sheets, using a coordinatograph. Examining these two alternatives it becomes apparent that the second offers more advantages. Not only is the first more expensive, but also it does not lend itself for streamlining the operation as well as the second method. Using a coordinatograph for coordinate reading would allow for as little change as possible in the routine duties of the B-8 operator. Just as he used to drop the points on the template material for laydown, he would do the same with the only difference of not having to use a different segment of material (template) for each model. Instead, he can use a large sheet, and employing pencils of different colours, he simply advances the sheet a few inches every time he records a new model. In this manner savings are realized both in material and in the time required on the coordinatograph. One automatic coordinatograph with one person may be able to process the outcome of four or five B-8's. The operator of the coordinatograph would be thoroughly familiar with the format for succeeding programs and data can thus be handled with a minimum of errors. The coordinates of the points are then obtained on cards ready for use in the numerical phase.

NUMERICAL OPERATIONS The objective of the numerical phase of the method is simply to bring the independently measured models to fit one another and the available ground control, using a suitable form of transformation. Perhaps the best way to present the various investigations into methods of numerical adjustment is to report the test data utilized and the results obtained. Test area

It is very important to emphasize at the outset that no particular test areas were planned for this method, but rather an actual portion of a previous mapping project was selected, thus imposing the most severe test of the method. From the first Nigerian project, which has been successfully completed (using stereotemplates), an area composed of five strips with a total of 91 models and containing 11 control points was chosen for the test (Fig.l). Since our interest was Photogrammetria, 23 (1968) 149-161

152

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• 5057

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15019

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mainly in a feasibility study, all numerical computations were performed on data obtained from materials already used in the project, i.e.: (1) No model set-ups were made especially for the method, and instead the old master stereo-templates were used. (2) The stereo-templates were made at a 1 : I ratio of the scale of the photography (i.e., at a 1 : 40,000 scale). Also note that in the B-8 the models were set up at twice the photo-scale (i.e., I :20,000) and then reduced by half (i.e., to 1 : 40,000) through the pantograph to the templates. Coordinate measurement

Again, because we wanted to find out first whether the method under consideration is feasible, the coordinates were measured off the stereo-templates on a Haag-Streit coordinatograph and recorded manually. The least division on the coordinatograph was 0.1 mm and the reading was estimated to 0.01 mm (or 12 ft. and 1.2 ft., respectively, on the ground). However, because of the nature of the small holes pricked in the templates, the pointing error is estimated to be in the neighbourhood o[ ± 5.0 ft.

MODEL ASSEMBLY INTO STRIPS Although it is theoretically possible to use the coordinates obtained from the coordinatograph directly in a simultaneous block adjustment, it would be an extremely slow and uneconomical operation owing to the great differences between Photograrnmetria, 23 (1968) 149-161

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153

the ground control system and the various coordinate systems of the independent models. Consequently, the closer the raw coordinates can be brought to the ground coordinate system, the more economical the adjustment would be. To satisfy this objective and to introduce more flexibility to the adjustment, a computer program was written to successively transform model coordinates to form strips and, at the same time, transform the strips approximately to the ground coordinate system. Simple linear transformation equations, allowing for a shift, a rotation, and a change of scale, were applied to match the three tie points between successive models. Although the redundancy in the solution is only one point, or two equations, Table I gives a good indication of the amount of discrepancies between successive models. TABLE I DISCREPANCIES B E T W E E N SUCCESSIVE MODELS A F T E R BEING ASSEMBLED INTO STRIPS 1

(SCALE 1 : 40,000) Strip (no.)

1

2 3 4 5

No. of models

19 18 18 17 18

Mean discrepancy

R.M.S. discrepancy

E

N

vector

E

N

vector

2.9 4.3 5.2 3.6 3.0

5.2 3.4 4.5 3.8 3.4

6.0 5.5 6.9 5.3 4.5

4.0 7.9 7.1 4.4 4.4

7.0 4.7 5.6 5.4 5.4

8.1 9.2 9.0 7.0 7.0

1ValuesgNenin Bet. It is apparent from Table I that the positional R.M.S. residual discrepancy between models is less than 10 ft. in all five strips. Nonetheless, the maximum value of the discrepancy reached 5 0 - 6 0 ft. in some spots, though very few. The question then arose as to whether these localized large discrepancies, caused by measuring and/or identification errors, would introduce serious breakage of the strips and prevent the possibility of adjusting the strips independently if need be. This question led to the following study of the behaviour of strips formed by analytical connection of independently measured models.

STRIP BEHAVIOUR

It was fortunate to have within the Nigerian project one strip composed of 20 models and which contained six horizontal control points. This strip was first subjected to a linear transformation holding to two points at both ends, as shown in Fig.2A. The residuals in this case, though large and between 100-200 ft., show a reasonable trend and do not indicate serious strip breakage. Next, the strip was adjusted through a second degree transformation holding to three points, one at Photogrammetria, 23 (1968) 149-161

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E.M.

MIKHAIL

L. A

r

- 1

5L; I

B

L C @ CONTROL USED

o CONTROL NOT USED

SCALE OF RESIDUALS

I---t 0 100

q 200 ~-T

Fig.2. Behaviour of a strip formed by analytical connection of independently measured models. A. Linear on two points; B. second degree on three points; C. second degree on all points.

each end and one in the middle, as shown in Fig.2B. The residuals on two of the three check points were reduced to acceptable values while the third (point No. 11) was about 90 ft. Rechecking the output from the model assembly program revealed that there was a discrepancy of some 60 ft. at the location of that control point. There was no time to go back and remeasure the coordinates at that location. Finally, the strip was adjusted by second degree transformation holding to all six control points as shown in Fig.2C. The results, as expected, indicated slightly better and more evenly distributed residuals except for point No.11 which still exhibited a residual of 70 ft. Although only one strip was studied, the results obtained were good enough to encourage further investigation, especially because of the severe conditions imposed by the type of data used. The rest of the study, therefore, was devoted to block adjustment by different methods including that by strips.

BLOCK ADJUSTMENT BY STRIPS

At the start of this investigation the opinion was held that strips built by analytical attachment of successive models would not conform to smooth curve behaviour and therefore would not be suitable for adjustment by polynomials. However, though limited in scope, the results shown in the preceding section indicate that this opinion is only partially valid. Consequently, to convince one's self of the actual behaviour of such strips, it was decided to perform block adjustPhotogrammetria, 23 (1968) 149-161

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ment by strips using the well k n o w n programs developed by SCHUT (1961) of the National Research Council of Canada. Three tests, with varying amounts of ground control points used as ties, were performed on the five-strip block shown in Fig. 1. Fig.3-5, as well as Table II, display the results of these tests. The residuals TABLE II COMPARATIVE RESULTS OF BLOCK ADJUSTMENT BY STRIPS USING D I F F E R E N T AMOUNTS OF CONTROL 1

Adjustment on 5 control points

R.M.S. Mean Std. dev. from mean R.M.S. Mean High residual No. of residuals

control used

control not used

11.0 10.6

53.0 51.3

2.7

13.5

1.03

1.03

15.0

66.1

5

10

Adjustment on 6 control points

ties used

Adjustment on all control points

control used

control not used

22.2 17.0

16.1 13.3

50.1 46.6

22.2 16.9

22.1 19.4

22.5 17.4

14.3

9.1

18.4

14.3

10.7

14.2

1.31 97.8 282

1.21

1.07

31.6

62.3

7

8

ties used

1.31

control used

ties used

1.14

100.3

46.8

282

15

1.29 99.1 282

1 Values given in feet. on all the control points were plotted, whereas only residuals that are equal to or m o r e than 25 ft. on the tie points between strips were plotted. T h e control points

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o CONTROL. USED • CONTROL NOT USED • TIE POINTS

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SCALE OF RESIDUALS 6

5~) IO ' OFT

Fig.3. Block adjustment of whole strips using five control points. Photogrammetria, 23 (1968) 149-161

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E.M. MIKI]AIL

held to are shown by hollow circles, those carried as check control by black circles, and tie points by small squares. At the points where two or more residual vectors appear, the difference between them gives an indication of the small discrepancy remaining between successive models since no averaging was performed. Fig.3 represents the case where five control points around the perimeter are used. Understandably, the residuals on the 5 control points used are small simply because the degree of redundancy is weak. It is also noticeable that the three check control points at the lower center of the area exhibit about the same residuals both in magnitude and direction. Consequently, on the assumption that there may be a somewhat constant creep in the central area for lack of tie control, the second test was performed using the same five points and adding the one point in the center. The results are shown in Fig.4, from which it is apparent that no 0 C O N T R O L USED • •

\

\

C O N T R O L N O T USED T I E POINTS

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,i

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S C A L E O F RESIDUALS 0

50

100 ' F'T

Fig.4. Block adjustment of whole strips using six control points.

appreciable change took place. Fig.5 shows the results obtained when all control points were used in the adjustment. Naturally in this case the residuals on the control points are smaller in magnitude, but what is interesting is that they are about equal to those on the tie points. This can easily be seen from the comparative results displayed in Table II for all three tests. One important observation from that Table is that the residuals on the tie points are practically the same, irrespective of the number of control points used in the adjustment. This indicates that the relative accuracy between strips depends, on the major part, on the number of tie points between strips, while the absolute accuracy of the adjustment is a function of the number of control points used. One of the most important features of the block adjustment by strips is the Photogrammetria, 23 (1968) 149-161

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157

O CONTROL USED • CONTROL NOT USED • TIE POINTS

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? ¶

--!

Z "o I--

AI

d

SCALE OF RESIDUALS (3

100 FT '

56

Fig.5. Block adjustment of whole strips using all control points. fact that when the results are examined, preferably in graphic form, erroneous data can be easily detected and eliminated. As an example, examining the residuals in the central east area in any one of the preceding three tests (Fig.3, 4 or 5), one would suspect that tie point No.268 is erroneous. To verify this, the last test in this phase was re-run excluding point No. 268 as a tie point but carrying it as a pass point. The results are shown graphically in Fig.6 and the new values of the O CONTROL USED • CONTROL NOT USED • TIE POINTS

\ D

J

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SCALE OF RESIDUALS () 5'0

100 FT '

Fig.6. Block adjustment of whole strips using all control points (point 268 not used as a tie point between strips).

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E.M. MIKHAIL

TABLE III E F F E C T O F E L I M I N A T I N G A GROSSLY ERRONEOUS POINT I

R.M.S.

Std. dev. /rom

Mean

R.M.S. mean

High residual

No. of residuals

1.16 1.18

49.8 52.8

15 278

tHe(Ill

Control used 23.4 Ties used 17.8

20.2 15.1

11.9 9.4

Residual on withheld point No.268

135.8 ft.

1 Values given in feet. accuracy measures in Table III. From these it is obvious that point No.268 was in fact erroneous by about 136 ft., and its removal as a tie point from the adjustment resulted in the reduction of the R.M.S. on ties from 22.5 to 17.8 ft.

BLOCK ADJUSTMENTSBY SEGMENTS OF STRIPS Although the results obtained from block adjustment by strips were reasonably good under the circumstances, further investigation into other methods of block adjustment was pursued. The objective of this phase is to determine whether the use of strip segments (six or seven models each) as units in the adjustment would further improve the results. Consequently, each of the five strips was divided into three segments, and the same block adjustment program used, only this time on fifteen short strips. No attempt was made to designate higher weight

o CONTROL USED CONTROL NOT USED • TIE POINTS

f/

\

\

\

SCALE OF RESIDUALS 0 5'0 lC)0 FT

Fig.7. Block adjustment of segments of strips using five control points. Photogramrnetria, 23 (1968) 149-161

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AEROTRIANGULATION WITH HORIZON CAMERA PHOTOGRAPHY AND B-8

o CONTROL USED • CONTROL NOT USED • TIE POINTS

/ o

l(

~

Ik o

Ix

-....

"~.

SCALE OF" RESIDUALS () 5b

IbOFT

Fig.8. Block adjustment of segments of strips using six control points. O CONTROL USED • CONTROL NOT USED • TIE POINTS

,/ /*

d

iff

it~

,(

I,

SCALE OF" RESIDUALS

x

E) 5 0

100 FT

Fig.9. Block adjustments of segments of strip using all control points.

factors for connection between segments of strips (i.e., along strip axis) than those for tie between strips (i.e., across strip axis). This way, more degrees of freedom were allowed to facilitate the detection of possible improvement in the overall fit of the block. The same series of three tests were performed in this phase; i.e., using five, six, and all control points, respectively. The results are shown graphically in Fig.7-9 and numerically in Table IV. The striking difference between these Photogrammetria, 23 (1968) 149-161

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E.M.

MIKHAIL

T A B L E IV COMPARATIVE RESULTS OF BLOCK ADJUSTMENT BY SEGMENTS OF STRIPS (6 OR 7 MODELS EACH) USING DIFFERENT AMOUNTS OF CONTROL 1

Adjustment on 5 control points

Adjustment on 6 control points

control used

control not used

R.M.S. Mean Std. dev. from mean R.M.S.

2.4 2.2

46.7 44.2

9.2 7.6

5.8 4.5

43.6 42.2

9.2 7.6

11.6 10.1

9.8 8.2

0.7

15.1

5.2

3.7

11.0

5.3

5.8

5.3

Mean High residual No. of residuals

1.05

1.22

1.30

1.22

1.15

1.19

1.06

3.3

61.0

5

10

ties ,sed

25.l 297

control used

control not used

A d j . s t m e n t on all control points

1.03

11.9

63.7

7

8

ties ,sed

25.2 297

control used

22.8 15

ties ,sed

25.8 297

i Values given in feet.

figures and those for block adjustment by strips (Fig.3-5) is the very small number of tie points for which residuals are plotted. The reason for this is, that since only residuals more than 25.0 ft. in magnitude are plotted, most of the tie points exhibit residuals less than this value. This, in turn, indicates that the internal fit of the block has improved considerably as it is given more freedom of movement by the use of short strips. Examination of Table IV and a comparison between it and Table II leads to the following remarks: (1) The use of segments of strips reduced the R.M.S. on tie points by more than half (from approx. 23 ft. to approx. 10 ft.). (2) The use of segments of strips reduced the R.M.S. on check control points by a factor of about 13 %, and for the case of using all control points in the adjustment this factor is almost 50%.

BLOCK ADJUSTMENT BY SMALL SECTIONS

It was originally planned to test the same data on a program for block adjustment by small sections (one or two models each). However, owing to a change in employment by the author toward the end of this investigation, this was not possible. Nevertheless, from the trend of improvement exhibited between adjustment by strips and by segments of strips, one may suggest in case of adjustment by small sections that: Photogrammetria. 23 (1968) 149-161

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(a) A further improvement in relative fit is likely, since the degrees of freedom would be largely increased. (b) A further improvement in absolute fit cannot easily be ascertained unless actual tests are performed.

CONCLUSION Despite the limitations of the data used and tests performed, the foregoing results indicate that the method of horizonal aerotriangulation by independent models applied to superwide angle photography and horizon pictures, is feasible both as regards to accuracy and economy. Furthermore, when this method is used in actual production, considerable gain in accuracy is likely if the models are plotted directly on the B-8 table at double the photographic scale; i.e., without the use of the pantograph. It is therefore recommended that further tests be performed on this method.

ACKNOWLEDGEMENT The author expresses his personal gratitude and sincere appreciation to Mr. J. J. Therrien of the Topographical Division, Department of Mines and Technical Surveys of Canada, for his limitless assistance throughout the course of this investigation.

REFERENCES

INGHILLERI, G., 1964. Some experiments of semi-analytical triangulation. Photogrammetria,

19:273-274. ScrlUT, G. H., 1961. A method of block adjustment for horizontal coordinates. Can. Surveyor, March 1961:376-385. THOMPSON, E. H., 1964. Aerial triangulation by independent models. Photogrammetria, 19: 262-265. WILLIAMS, V. A. and BRAZIER, H. H., 1964. Aerotriangulation by the observation of independent models (A I.M.). Photogrammetria, 19:275-278. ZARZYCKi, J. M., 1963a. Super-infragon photography and auxiliary data on a mapping program for Nigeria. Can. Surveyor, 17:13-26. ZARZYCKI, J. M., 1963b. New aerial triangulation techniques employed on a mapping project in Nigeria. Photogrammetric Eng., pp.692-701. ZARZYCKI,J. M., 1963c. Experience with a new mapping system employed on a topographical survey in Nigeria. Con[. Commonwealth Surv. Officers, Presented Paper, 50:10 pp. ZARZYCKI, J. M., 1964. The use of horizon camera, doppler navigator, and statoscope in aerial triangulation. Congr. Intern. Soc. Photogrammetry, lOth, Lisbon, Presented Paper, 30 pp.

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