Compensation of systematic errors of image and model coordinates

~oto#~,,met~ s7 (1981) 1~--44 Blmvier Scientific Publkhins Company, Amstmdsm -- Printed in The Netherlands .

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COMI'BNSATIONOF!BYIb'TIgMATIC ER,ROItS OIP IMAGE AND MODgL COORDINA"I"ll + +

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Hekin&i Unllmmdty+ofT+¢hnolo4ty, Institut# of Photoirmmmetry, 02160 Espoo 15 (Finland) (Received November 6,+1980; aa~pted April 15, 1981) ABSTRACT KilpeU/, B., 1981. Compensation of myst,aatlc errors of ~ P h o ~ , 87:15-44.

and modql coordinates.

An effort has been made to evaluate different approaches in compenmtinl systematic errors (with respect to the funational model applied) in a e r o ~ t i o n . The main object of i n ~ has been the comperison of component calibration, test field calibration, and self eslibrat/on. The study has been carried out empirically. Rather extensive test fired data have been app!ied. Severs1 institutions have pmrtieipeted in the meuuring and cor~puting work. The report summarizes the result8 obtained.

1. INTRODUCTION The development of the methods of aerial triangulation in a more rigorous direction during the past decades has given the systematic errors c~f observations (with respect to the functional model applied) a decisive rol~ in terms of the accuracy and the reliability of results. In consequence, a n~niber of different approaches P,o the problem of systematic errors has been introduced in many individual studies. In order t~) obtain comparative lmow'-.edge of the compensation methods, a working group was established within Commission III of the ISP in accordance with a resolution made at the XIIIth Congress of the ISP in Heisinki 1976. The WG ~et as it~ goal to supply more information on the compensation of the systematic errors of image and model coordinates in different aerotriangulation methqzts. An agreement was made to take into account both accuracy and, aq far as possible, economic aspects. It was also agreed that a comparative study of component, test field and self calibration methods should be carried out using real data, i.e., empirically. Further, the triangulation methods with independent models and bundles were to be the most important methods investigated. The attainment of the goal of the WG has required a considerable effort

0031-8663/81/0000--0~)001502.75 © 1981 Elsevier Scientific Publishing Company

from the participants in test field photography, measurements and computation. The following nine organiza~ions participated in the activitiesof the W G : - South Australian Lands ]Department, Adelaide, Australia Laboratoriet for fotogrm,.nmetri og landm~ling, Aalborg Univezsitetscenter~ Denmark • - Institut ftir Photogrammetrie, Universi~t Bonn, FRG - Institut fiir Photcgramrnetrie und Ingenieu~.ermessungen, Techni~:he Universitb't Haunover, F R G - Lehrstuhl fiir Photogrammetrie, Technische UniversitA't Miinchen, FRG - Institut fdr Photogrammetrie, Universitiit Stuttgart, FRG - Ins~.tute o f Photogrammetry, Helsinki University of Technology, Finland -

. National

Board

of Survey,

Hels~nki,

Finland

Ge~tetical and Geophysical Research Institute of the Hungarian Academy of Sciences, Sopron, Hungary For planning and coordinating its work, the WG organized meetings hl ~;tuttgart and Moscow ia 19'17 and 1978, respectively, In addition, a seminar ~or reviewing and evaluating the preliminary results obtained was arranged in ~alborg in 1979. As to the execution of the study, directions for measurements and computatic, n were prepared in order to guarantee uniform and comparable final results. : h:,wever, the choice and application of triangulation and compensation m~i~hods were not touched upon; every participant was given a free hand in tb~s respect. This had the result that aJl methods were no~ treated equally. E.g., the method of independent models had to be omitted because of an insufficient amount of results. Likewise, the treatment of component calibration remained inadequate for the same reason. Further, it was found in the course of the study that a discussion of economic aspects would have been premat, lre i:n this context, and, consequently, they have not been dealt with in this report. In closing, it is worth mentioning that, in addition to this report, several papers which refer to WG IIIi'3 were submitted to the Hamburg ISP Congress. Both the theory of ,compensation and empirical results are discussed in them. -

2. STUDY MATERIAL

2. 1. Test field

Photography over four test fields located in Australia and Finland was used in the studies of the W G (Table I). Aitltest field points used as control ot check points in photogrammetzdc adjustmer~ts have been coordinated by ground survey. The coordinates have been transformed for this study into a rectangular (cartesiml)coordinate system, which makes the correci~cns for earth curvature and map projectior~ superf/uous. In addition to the co,~dhmted points, o~ the boarders of the J~mij~,i

17 TABLE I Specifications of the test fields Test field

Country

Size a (kin 2)

Max. height diff. (m)

No. of points b

Accuracy (mm) planimetry height

Willunga Kapunda Jiimi'~rvi (f~nall) Jmij~Ti ( l a r g e )

Australia Australia Finland Finland

5.8 x 5.8 24 x 24 0.8 x 0.8 2X2

130 300 25 60

25 e 40 e 5d 3d

96 43 180 121

30 e 40 e 0.6 mm/km 0.6 ram/kin

a Area of the coordinated points. bNo. of the coordinated points. ©Average stlmdard error of one coordinate. dMaximum standard error of one coordinate. (large), Willunga and K a p u n d a test fields there are 100, 28 and 70 additional ( u n c o o r d i n a t e d ) points which enlarge the test fields to cover an area of a b o u t 2.6 X 2.6 k m 2, 3 X 3 krn 2 and 4 0 X 40 km 2, respectively. Both the c o o r d i n a t e d and the additional ( u n c o o r d i n a t e d ) points o f the test fields were provL:led with targets ( F i g . l ) . Generally, it can be stated t h a t the targets of the Australian test fields were well visible in the p h o t o g r a p h s . As for the J~irnijiirvi test fields, the identification of the ~argets was s o m e t i m e s troublesome.

a) J3mij;~rvi (smal I)

b) J:imij3rvi (large)

c) Willunga

!.20 m __%3_~ m

0,60 ,n . ~ _~-__0_,_~_o ~,, ~ I

d) Kapunda 2.40 m

0.39

m

q,20 m

2.30 m

m

"1 ~

fluorescent)

Fig. 1. Target types used in the different test fields.

2.2. Photo material The p h o t o m~te~al used by the WG was quite versatile; there was a fairly large rm~ge of image scales and block sizes. F u r t h e r , b o t h reseau a n d nonreseau photogTaphs were available (Table [II).

(}I G2 G3 HI H2 H3

F3

Univ. Stu~gart, FRG

J~'~, large

Helsin~ Univ. of Techn., Finland

E] E2 E3 F5

PSK 1

PSK 1

J~Lij~rvi, large

TU Miinchen, PlaniFRG comp C-100 PS~

C1 C2 C3 D1 D2 D3

large

J~m"y~rvi,

Kapunda

"+7~lunga

FSK 2

~ d s Dept. Adelaide, Australia AFt

RMK A2

P.MK A2

RMK A2

~

1 : 4 000

! " 4 900

1:4 000

1:50 000

1:12 OOO

EW

SN

EW

SN

EW

SN

EW/WE

EW WE

20 • 20 • 60 20: 203 60

60 20" 20 • 60

20'

~2

202 20" 60 20" 20" 6O

202 203 60 20" 20 ~ 60

Side

h~

Flight

dire¢~

A1 A2 A3 B1 B2 B3

Scale

Test field

Instr.

institute

Came 'a

Specifications of the measured material

Me~.su~ment

Data ~t symbol ~

Suecifications of measurements of block photographs

TABLE II

3 3 6 4 5 9

strips

No. o f

24 24 48 24 24 48

24 24 48 24 24 48

45 25 24 49

9.2

24 ~t 48 36 45 81

photos

Glm

Film

f~m f~n neptives

Meamrements

Disp ositive matt~ial

PSK 1

PG 2

J~v', large

J~nijiirvi, large

MRB

MRB

1 :4 000

1 : 4 000

EW

EW

20 s 20 ~ 60

20: 20: 60

J'~miji/rvi, large J~mi~/rvi, larg~ Jiim~, small

J ~ f i j ~ v i , largo ~ , large J ~ , small

Kapun~ W~fllunga

ItMK A2 (WA)

MRB (WA)

RMK AR (WA,

'INvo cross-flight block~ : Alternating flight direction~

Fesea~l )

Tc~t field

C~era

Photographs available for the WG

TABLE HI

block block

block strip strip

block strip strip

Type of photogr,

1 : 50,000 1:12,000

1 : ~000 1: 8000 1:4000

1:4000 1:8000 1: 4000

Nominal scale

EW/WE: EW

SN, EW~ SN, EW: SN, EW:

SN, EW ~ SN, EW ~ SN, EW ~

Flight direction

6+6 1+1 1+ 1

60/60

60/60 60/60

80/ 80/

9 6

6 +6 1+ 1 1÷1

60/60 80/ 80/

No. o f strips

Forward/ side lap

: Symbol is used t~ i~ent~y the data sets when presenting the results of block adjustmmats. =Odd numbered strips. Even numbered strips.

,,

Nat. Board of Survey, Helsinki, Finland

J1 J2 J3

,

Geod. and Geophysical Inst., Sopron, Hungary

I1 I2 I3

Date of photogr.

20 23 43

81 48

31.03.76 15.01.75

48 + 48 16.08.77 3 + 3 16.08.77 3 + 3 16.08.77

48 + 48 16.08.77 3 + 3 16.08.77 3 + 3 16.08.77

No. of photos

3 3 6

24 24 48

Glass

Film

Helsinki Univ. of Techn., Finland

M1 M2 N1 N2

R1 R2 $1 S2

Q1 Q2

Geod. and Geophysical Inst., Sopron, Hungary

T U Munchen FRG

K1 K2 L1 L2

P1 P2

instivate

Measurement

symbol

set

Data

~ :8000

!: g000 1 :8000

1 °4 0 0 0

1: 8 0 0 0

1:4000 1:8000

J~mij~vi, large

J/tmij~rvi,small J~nij~rvi, large

small

J~ij~rvi, Jgmijgxvi, large

J~m.ij/iwi,small )/irnqfirvi,large

RMK A2

MRB

PSK 1

PK 1

MRB

1" 4000

J~ni'~rvi, small

RMK A2

PSK I

PG 2

Scale

Test field

Camera

in~r.

Specification~ of measured material

Specifications of measurements of strip photographs

TABLE IV

Film

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

SN EW SN EW SN EW SN EW SN EW SN EW SN EW SN EW

Film

Glass

Film

Diapom.~ive material

Flight No. of dir~et;.~.n ph-~t~

0

21

With regard to the photography, attention should be paid to the followi~g fact~: (a) In each case the flight p r o e m w ~ carried out in one day. (b) Strip photographs flovm over t~.~.eJiimijiirvi test fields are intended only for test field calibration. (c) F o r t h e J ~ / i r v i mission, the RMK A2 and MRB cameras were mounted in the same ~ , which re~ultecl in nearly :gtmultaneous photography. (d) In the Jiimijirvi blocks, cidv overlap between some strips is only 55% (10%), "mste,~i of 60% (20%). ~ led to a ~arcity of tie points, pariicularly in blocks with (nominal) 20% side overlap. The laboratory procedures applied were those used in standard production. The Kapunda and Wfllunga photo material was prepared for measurements by the South Australian Lands Department and the J~nijiirvi material for measurements by the Finnish National Board of Survey and the Helsinki University of Technology. 2.3. Measurements Altogether, six institutesparticipated in measuring the photograpb~ for the W G (Tables II and IV). The Australian photographs have been measured for other than W G purposes already in 1975. Therefore, there are some differences in the measuring 9rocedure as compared with that of the J~nijiirvi photographs. In the fo~owing, a brief description of both procedures is given: (a) the Kapunda told Willunga photography (reseau), (1) Measurements were made from the original film negatives. (2) One pointing was made on both targets and reseau crosses. (3) 25 evenly or n~arly evenly distributed reseau crosses were observed. (b) the J~-nijiirviphotography (1) Observations were made in two rounds. (2) Fiducial marks were observed at the beginning of the firstround and at the end of the second round. (3) 4 and 20 fiducialmarks were measured from the photos taken by the R M K A2 and M R B , respectively. (4) The use of the ISP standard test was rec¢ mmended in connection with the metsurements, in order to evaluate the accuracy of the measuring ir~struments used. 3. COMPUTATION

3.1. Compensation methods The data measured were cc,mputed in seven organizations. Each participant was ~.~eeto choose the data he was interested in ~nd the triangulation and com~ensation methods he wanted to use in processing them {Table V). With re~s,d ~o compensation, the computation carried out can be divided into

22

TABLE V Participants in compt ration, and methods and data used by them ]Institute

Triangulation method

Calibration method

Data used

Geod. and G~mphysica] Inst., Sopron, Hungary

anblock

self

E3, F3, I3

Helsinki Univ. of Technology, Finland

bundle

component, test field, self

A2• A3, J1, J3

TU Miinchen, FRG

bundle

test field, self

J3 AI--A3, El--E3, FI--F3

A3, B3, C3, D3

AaLborg Univ., Denma~k

bundle

self

Univ, Bonn, FRG

bundle

self, test field, A3, J3, El--E3, F1--F3 component

T U Hanover, F R G

bundle

self, component

A1--A3, EI--E3, F1--F3

Univ. Stuttgart,F R G

bundle

self

A1--A3, BI--B3, GI--G3, HI--H3

four gToups: (1) reference adjustments; and adjustments involving (2) component calibration; {3) test field calibration; or (4) self calibration. These concepts are briefly defiv.ed in the following. Reference adjustment

Reference adjustment is taken to mean an ordinary adjustment where no special effort is made to compensate systematic errors. It is to serve as a measure when evaluating the effectiveness of compensation. For reference adjustment, the following steps are taken: (1) Affine transfor~nation wi th 6 parameters on 4 fiducial marks. (2) Correction of mean symw~etric radial distortion according to calibration report. (13) Correction of refl'action according to Bertram's formu!a. (4) Weight p = i i,~ give, to al~ o~,servations and weight p - ~ {infinity) to the ground control point:~. Each participant has applied reference adjustment to every project parameter combi, nation (overla#~;, fligh~ direr: ~ion, c3ntrol version) he h,,s used. C o m p o n e n t ca~i 5 : ~:~tion :

Compensation n:~:~3~ares have b~,en referred to c o m p o n e n t calib~at?lo~, if:

23 (1) data refinement differs from that for reference adjustment; and (2) no other calibration method has been applied.

Test fleid calibration In this context, test field calibration includes the cases where the calibration data applied to compensate the systematic errors of a block are determined from: (1) a ~eparate test field photography (e.g., strip photographs of the small and the large test field of J~mij{Lwi); or _from (2) a sample of block photos by t ~ a t i n g the test field points appearing on ~hese photos ~ known points (e.g., closeness with lvspect to time and place~. The latter case tends to simulate an ideal case of test field calibration, in which the test field is situated in the project area.

Self calibration The gvneral terms, self calibration is a process, in which the compensation of systematic errors of the data is based on information extracted from the same data only, i.e., no external information is required. This definition includes simultaneous self calibration, in which calibration is accomplished by extending the functional model of the triangulation method ~o cover the effect of systematic errors, as well as a.posteriori self calibration, ~Jhere compensation is based on the analysis of residuals of observations and the reexecution of adjustment by using improved observation~ data.

3.2. The practice of computation Each participant was provided with the following material for computation: (1) Comparator (or model) coordinates. The institutes which carried out the coordinate measurements were asked to clean them from gross errors by using their own methods. Any further elimination of gross errors in the in.'.~'*utc~ performing computations should have been avoided to obtain comparable results. However, some institutes did not fully follow this suggested course. It naturally caused some difficulties in the analys~s of results. (2) Calibration report. The aerial camera RMK AR had been calibrated at C~l Zeiss, Oberkochen, three years before the test flights, i.e., in 1972. The cameras MRB as well as RMK A2, in turn, were calibrated at Cazl Zeiss, Jena, ~ ( i at the Helsinki lJniversity of Technology, respectively, just before the flights in 19,77. iSach calibration report contains the following ~]'fformation: (a) coordin~ltes of fiducial marks (or reseau crosses); (b) calibrated focal length; and (c) radial distortion on four semi-diagonals. In addition to these, tangential distortion and some other calibration data were determined for the aerial cameras MRB and RMK A2. (3) Object coordinates referring to a rectangular (cartesian) ~oordinate system. (4) Recommendations for control point patterns. Three different control patterns w~re recommended for blocks (Fig.2a). For test field ,~a]ibration,

's4 l)

0

0 0 0 ~ 0 0 0

o

0 B1

0

0 ,' 0 Z

ooo

B2

S3

~~-O0000Z ~O0000Z ,. ,

oo ooo

&O0000~ ,~00000~ e~

/

e5

• xyz-cont rO~ Doint l-control

Ooi.t

Fig. 2. a. (~ontrol p a t t e r ~ r e c o m m e n d e d for blocks, b. Control p~tterns for 131vck3 ~ e d in addRion to the r e c o m m e n d e d ones.

also three point-scheraes w e ~ ~ecommended: (a) version $ 1 : 2 5 evenly distributed points; (b) version ',~2:64 evenly distributed points; arid (c) version $3: all avmlable points. To guarantee a high standard of uniformity, participants were even provided with listsof control po:ints.It wes, however, impossible to follow these listsexactly in all cases, but tl,esam ~ p~ttern form was always preserved. In addition to the control patterns given in Fig.2a, participants were free to use p~itternsof their o w n (l~'ig2b). As seen from Fig. 2a, b, contro( pattern B1 is extremely sparse with regm'd to height; on the contrm'y, patterns B3 and B6 tirevery heavily controlled. Pal:t.~l~s B2, B4 and B5 are in good correspondence with practical applications. (,~.)Instructions for the presentation of results.The instructions given incb~ded formulas for computing the root m~:an square error ( R M S E ) ~t check points {i.e..the discrepmlcy betv~een geodetic and photogrammetric determination), ~a~hichserves as the prin~ary ~eans to measure the ~ff~ctive. ne.~s of compensa~oion.

25 ++ I

I12

(/~y and ~z accordhlgly)

where: m = nominal ~cale of photography (cf. Table III) Xp pho~grammetric~y dete~ined ground coordinate Xg "- geodetically d e t e ~ m e d ground coordinate l number of checkpoints in the block in question 4. RESULTS

4.1. General

In the following, the results achieved by the WG will be grouped in accordance with the compensation methods used. In the discussion of the results, atbmtion has been paid to those factors that have a-priori been considered to be important for the compensation of systematic errors or that have proved to be so. When evaluating the results to be presented in this paper, the following facts should be taken into account: (a) In this context, only the most evident trends seen in the l:e~ults have been reported; many interesting details included in the original results have been omitted. They can be found, to some extent, in the separate, reports of the different participants. (b) The reliability of the findings and trends discussed varies rather widely due to the quantitative and qualitative variation in the original results from which they have been extracted. E.g. component calibration cannot be widely discussed, because there was only little interest in that method among the participants. (c) A comparison of the absolute accuracies achieved with the same data in the different institutes is somewhat difficult, because even the results of the reference adjustments differ (contrary to expectations) from each other in many cases.

4.2. 8elf calibration The largest part of the results presented by the participants of the W G have been achieved by simuh~aneous self calibration, i.e.,by introducipg the additional parameters into the adjustment to compensate for systematic errors and by estimating their values simultaneously with other unknow ~,parameters. Altogether, 14 different parameter ~ets were :ased in this study. The formulas of these parameter sets are presented i~ Appendix A. In the following, some comments (based on the references) are made on their typical features: {a) The additional pz~ameters ol sets b and h are mutually orthogonal and

26

also n,early o~thogonal to the elements of exterior orientation. The mutual orthogonality holds exactly for an evenimage point distribution of 3 × 3 and 5 × 5 points, respectively. (b) Parameters al ...a,2 of set a are nearly orthogonak and also neatly orthogonal to az3 . . . a , s . Among parameters a~3 ...azs there are a few moderately high correlations. (c) Also parameter se~.j is formulated so that the correlations between the parameters are slight. (d) Parameter set n, is the purest example of an error model in which the effect of different error sources are "svpamtely" modelled: in it there are pammet~rs for affinity and non-orthogonality (of the image coordinate system), i~ includes 5rown-Conrady model for decentering distortion and a polynomial of the ~eventh degree for radial distortion. Accordingly, this mo~lel c~m be referred to as a "physic~d model", TABLE Vl Comparison of the performance of the different p~ramet~r s~ts in blocks with 20% aids overlap and control patterns B5 or B6. Significance testing or weighting not applied. Computed in Bonn Data

Parameter

S¢' t

~,!IL

Control B5 (medium) so

iI~MSF~ (~m)

Control B6 (dense) Impr. (%)

(~m) E1

#xy

#z

#xy

~z

~'xy

~t:z

3.4 2.9 2.8 2.9 2.9

6.4 4.9 4.4 4.3 4.4

11.6 8.9 8.3 8.8 8.9

¢).3 31 33 31

23 28 24 23

3.8 3.1 3.0 3.1 3.2

3.7 3.3 3.2 3.2 3.4

8.0 7.4 7.2 7.3 7.2

11 14

10

14 8

10

i d

3.6 2.9 2.8 2.9 3.0

6.9 6.2 4.5 4.6 3.9

13.4 8.8 8.2 8.1 7.6

1~) 35 33 43

34 39 40 43

4.1 3.0 2.9 3.0 3.1

4.6 3.4 3.3 3.2 3.1

8.4 6.5 6.3 6.2 6.2

26 28 30 33

23 25 26 26

]~ef. : a ~ t ~i t' d

3.9 3.0 2.9 3.0 3.3

6.2 3.2 3.1 3.1 3.3

8.9 7.2 7.8 7.2 7.2

4;3 50 50 47

19 12 1~ 19

4.2 3.1 3.0 3.1 3.3

3.5 2.4 2.4 2.5 2.8

6.6 5.5 5.1 5.3 5.4

31 31 29 20

17 23 20 18

'~ef. ca::~e l a

3.5 2.8 2.8 2.8 2.9

6.1 4.5 4.0 4.1 4.2

9.9 8.0 8.3 7.9 7.8

2B 34 33 31

19 16 20 21

3.9 3.0 2.9 3.0 S.1

4.1 3.1 3.1 3.1 ~.3._~

77 5.9 5.9 57 5.6

24 24 24 24

23 23 26 27

F~ef. case

Ref. case ] ~L

F2

Impr. (%)

#z

a f dl

F]

RMSE (~m)

(~m) ~xy

1

E2

So

d

8 9

27

(e) The parameter~ in ~et c arethe coefficients of the function of spherical harmonics Ofthe thbd degree (with slight modifications: the constant term is excluded and the pa~zmeters for affinity and noworthogonality are included). Trigonometric func~ons appear also insets i, j, a n d k (mixed models). o n the basis Ofthe results by the WG, thefollowing general stm~ments can be made on self calibration" (a) The accuracy improvement ls cn an average 20--30% as compared with the reference (conventional) adjustment. However, the variation in reeu!~ is surprisingly wide. A t best, the results improved by 60--70%, but, on the other hand, in many cases they even deteriorated considerably. Table VII. which has been constructed on the basis of all the results of the WG, gives TA]~LE Vll Accurecy estimates for self calibration in different types of biock~. Figure~ (I1MSE~ in ~ ~ ) are based on all results obtained by the WG ~"-.....,

Side lap

Con t r o ] ' ~ " ~ Sparse Medium Dense

60%

20% . .xy

Pz

Pxy

~z

10--25 7--20 ~-'10

2.5--3.5 2.5--3.5 2.5--3.0

6--9 5--7 4--6

4--7 4--7 3--4

TABLE VIII Comparison of two orthogonal p~rameter sets b (12 parameters) and h (44 parameter0. Para~eters significant on a 95% l~.vel have been included in the compensation model. Computed in Munich v,,,,~,u, set

C3

J3

........... set

~o (pro)

,~,vJor~ (pm)

impr. (%)

/~xy

Pz

/~xy

Pz

B1 (sparse)

Ref~ case b h

4.6 4.1 4.0

5.2 3.8 3.6

11.5 7.2 6.5

27 31

37 43

B3 (dense)

Ref. case b h

4.8 4.2 4.1

3.9 2.8 2.6

6.7 5.5 4.5

28 33

18 33

B1 (sparse)

Ref. case b h

4.1 4.0 3.8

~_.3 2.7 2.6

12. t~ 10.5 7.5

37 40

13 38

B3 (dense)

Ref. case b h

4.3 4.1 3.8

3.5 2.6 2.8

6.5 5.7 5.0

26 20

12 23

28 some idea of the accuracy, obtainable by self calibration. (b) Contrary to expectations, the improvements were only slightly better in height ~han in planimetaT.

(c) No singleparameter mt has consistentlyproduced the best results. Some examples of the performance of the different parameter sets can be round in 'rabies e l , VHI--XI. The following discussion gives closer information on how accuracy improvement depe~nds upon: (1) the way of treatment of additional parameters; (2) the project parameters of the block concerned; and (3) a-priori data refinement.

T A B L E IX

Comparison of the performance of the different p~krameter sets in two ~!~cks with 20% side overlap and m~dium control (B2). Significance testing or weighting not applied. Computed in Helsinki Parameter set

WiIlunga A2, control B2 ~o

J~imij/irvi J2, control B2

RMSE (am)

Impr. (%)

#xy

az

axy

Ref. cage

,t.4

6.2

16.5

3.1

62

17.3

0

b

3.1 3.8 3.7 3.5

6.5 5.0 7.7 5.6

9.1. 12.8 28.0 9.2

-5 19 -24 10

h

m

Impr. (%)

#xy

az

,Uxy

az

5.5 4.0 4.0

10.9 9.1 9.8

27 27

3.9

3.9

9.4

29

3.7 3.9

4.5 4.0

8.8

18

9.9

29

17 10 14 19 9

(am)

a c

RMSE (~m)

So

(~m) ~z

....5 45 22 -70 44

4.0 3.6 3.9

TABLE X

Comparison of the performance of the different parameter sets in two blocks with 60% side overlala and medium (I]2) control. Significance t,~sting or weighting not applied. Computed in |telsinki Parameter set

Willunga A3, control B2 so

RMSE ( a m )

J~:nij~irvi J3, control B2 lmpr. (%)

(urn) Ref. case a b c h m

4.8 3.1 3.4 3.8 3.3 32

so

RMSE (am)

Impr. (%)

axy

az

#xy

#z

4.3 2.6 2.8 2.8 2.7 2.6

8.7 4.9 6.8 5.4 5.1 5.5

40 35 ~5 ~7 40

44 22 38 41 37

(urn) #xy

/~z

a:zy

/~z

4.5 2.7 2.7 3,0 28 27

8.5 5.3 5.4 4.8 5.0 5.1

40 40 33 38 40

38 36 4L.i 4!t 4()

4.4 3,8 4,2 4.1 3.8 4.1

29 TABLE X i Accuracy i m p l e m e n t s in p e r v e n t a p s (compared with resp. reference adjustment) ob~tined with different pmltmeter sets in two Willunga blocks with varying project parameters Parameter set

Side lap 20~ Control B8 ,

kI e2 b~ m~ a2

,

Side lap 6 0 ~ Control B1

m

~xT (A%) ~z(~%)

"xy(A%)

~z(~%~

18 12 17 17 12

42 35 40 42 40

56 56 57 57 54

29 8 13 18 23

I Significance testing not applied, weighting applied (©f. text). 2 Significance testing applied, weighting not applied.

Blo~:kwise versus stripwise parameters A series of bundle adjustments with the orthogonal pm,ameter set b, when introducing additional parameters common to: (a) all strips; (b) every other strip (subblock with 20% side overlap); and (c) the whole block, gave the following results: (1) If significance testing was not applied, the order of superiority was (c), (b), (a) in all cases. Particularly, stripwise introduction of additional parameters (case (a)) gave poor results: the deteriorating effect was often larger than 50%. (2) The application of significance testing clearly brought the results closer to each other, but the order remained the same in most cases. (3) The results were in good agreement with expectations: The le~s controlled the block (control points and overlaps), the poorer the results achieved by stripwise introduction of additional parameters. Significance te~ting of additional parameters Significance tests of additional parameters have been applied in Hannover (parameter sets i and j), Stuttgart (parameter set b) and Munich (parameter sets b and h). The pure effect of testing can be assessed from the results of the first t ~o institutes, as the results achieved without testing have also been reported. In Stuttgart the following procedure was applied: (1) Significant parameters were determined, by applying the one-dimensional t-test: from a block adjustment, where all ground points were treated as known points. (2) Parameters found significant on the 99.9% level were then introduced into the block adjustments of the data set concerned.

~O

Due to the orthogonality of the parameters (set b), prerequisites for the applicatfion of the one-dimensional t~test obviously exist. How~er, because of the treatment of all object points as known, the pn~edure u such k n o t operational. The results achieved by this procedure ~ e d out to ~ s i w ~ in all blocks adjusted: testing improved accuracy only when additional parameters were introduced strip wisely (Table XII). In Hannover, significance testing was performed in an o ~ way by applying the one-dimensional t-test and the significv.nc~ levels 67% and 95%. ~i'he ~sults were not very consistent (Table XIII), which may be an evidence of the strong correlat!~ between the parameters. :PAI~L E Xll

~&ccttx~cy improvements (%) achieved by applying sigrdflcance testing on additlona~ parmn,.~ters. Testing procedure as in Stuttgart (of. text), Data set A8 Control pattern

B1 B2 B3

Parameters common to Each strip

Two rash-blocks (20%) Whole bl!ock

P ~y

#z

Pxy

~z

~Lx'~' Pz

27 29 8

34 20 8

0 4 -4

0 2 0

0 0 0

0 0 0

T A B L E XIII

Accuracy improvements (%) achieved by applying significance testing on additional paxsmete~,,s. Testing procedure as in Hannover (of. Text). Data set A3 Control pattern

Sign. level 67%

Sign. level 95%

B1

0

1

0

8

B2 B3

0 0

0 --18

0 0

-20

7

|¥eightingof additional parameters Weightirg of additional p:m,:amel;ershas been applied in Aalborg and Helsinki. ~n both institutesthe principle of weighting has been the same: the weights b~ve been so determined that the effect of an addit:ion~ parameter is of the desired magnitude in a desired position on the image. i.a Hels~,nki fi~e. weighting tests have been carried out by usin ~ the Wfilunga data, and parameter set a. Th,~ weights used ~f~.~the aflclitional parameters

60

A3

See text.

20

A2

100 30 10 5 1

20

A1

Ref. ease all free 100 ~ m / 1 0 0 30 ~ m l l 0 0 10 ~ m / 1 0 0 5 ~m/100 1 urn/100

Kef. case all free 100 , r o l l 0 0 30 ~ m / 1 0 0 10 ~ m / 1 0 0 5/~m/100 1 Izm!100

Ref. case all free ~m/100 mm ~m/I00 mm ~m/100 mm ~m/100 mm #m!!00 ~

Side Weight ~ lap (%)

Data set

mm rnm mm nun mm

mm mm mm mm mm

4.8 2.9 2.8 2.8 2.8 2.8

7.1 6.8 6.6 6.6 5.8 5.5 5.3

5.5 9.4 9.3 8.0 7.2 5.6 4.5

17.1 7.8 7.8 7. ~ 7.7 7.6

35.5 46.1 43.6 22.3 21.4 17.8 19.2

20.3 45.6 35.5 ~ 26.0 17.7 17.6 17.4

40 42 42 42 42

4 7 7 18 23 25

-71 -69 -45 -31 -2 18

54 54 55 55 56

-30 -23 34 40 50 46

-125 -60 -28 13 13 15

4.5 2.7 2.7 2.7 2.7 2.7 2.8

6.2 6.2 5.9 5.5 5.5 5.0 4.5

5.5 10.8 10.5 9.9 6.3 5.1 4.4

Pxy

8.7 5.3 5.3 5.3 5.3 5.3 5.4

16.5 17.3 16.6 12.6 9.1 8.2 11.0

15.1 9.7 9.5 9.4 9.1 8.9 10.0

b;z

~xy

~xy

# ~.

RMSE (~m)

Impr. (%)

RMSE (~m) Pz

C o n t z ~ B2

Control B1

40 40 40 40 40 38

0 5 11 11 19 27

-96 -91 -80. -15 7 20

/;xy

39 39 39 39 39 38

-5 -1 24 45 50 33

35 37 38 39 41 34

Pz

Impr. (%)

3.2 2.6 2.5 2.5 2.6 2.6 2.6

4.2 3.6 3.4 3.4 3.4 3.4 3.5

4.6 4.0 4.2 4.2 4.1 4.1 4.2

/~xy

5.3 5.0 4.9 4.9 5.0 5.1 4.7

9.7 10.9 10.6 9.0 7.2 6.8 6.5

12.2 8.9 8.9 8.8 8.7 8.4 8.2

Pz

RMSE (~m)

Control B3

Effect o f weighting or. ~he accuracy obtained by self calibration. Willvnga data, parameter set a. C o m p u t e d in Hebfinki

TABLE XIV

19 22 22 19 19 19

14 19 19 19 19 17

13 9 9 !1 11 9

Pzy

6 8 8 6 4 11

-12 -9 7 26 30 33

27 27 28 29 31 33

Pz

Impr. (%)

go

32

correspond to displacements 1, 5, 10, 30, and 100 ~ m in the image point x = y = 100 ram. Table XIV shows the results, which are very hvourable, in a more detailed way: (a) Especially in weak blocks, the effect of weighting is very affirmative. This results,naturally, from an improvement in the condition of normal equations. (b) On the contra~,, it is important to notice that the results;do not deteriorate in heavily controlled blocks. (c) O n the basis of these tests,it seems evident that the optimum veights correspond to an image point displacement ~'fclose to 5 #m. In Aalborg all self-calibratingadjustments have been performed by applying weights which correspond to a displscement of 3 # m in the image point x = y = 100 ram. From the results reported, it is not possible to separate the mere effect of weighting, but, on very good grounds, it can be suspected that weighting has played an important role, when considering the good re~ults (especially in weakly controlled bloc~) obtained.

Consideration of c¢)rrelation8 In spite of the importance of correlations, frequently expressed, only one pa~icipant has tz'eat ~.d this que,tion. Table XV presents the few results. These offer, nevertheless, an example of the importance of the consideration of correlations, mid set forth th~ ~leec[ for further investigations. TABLE XV Example of the improveme~,ts obtained b y excluding the additional parameters correlating mutually more thtm 0.85. Parameter set j Computed in Hannover Data set

Control vemion

Improvement (%) ~Uzy

~z

AI

B1 B2 B3

2 2 ,i

84 6 0

A2

BI. B2

0 1

-41 71

A-priori data refiaement In order to study the effect of a-priori data refinement on the compensation of systematic eiTors by self calibration, a series o~ adjustments was carried out in H elsinki. T w o ,~ata refinement levels were used in the adjustments: (1) as in reference adjustment; and (2) 4.parametric tr~sformafion~ no a-priori corr~,~ctions.

33

Two comments can be made on the results: (1) on the whole, there is no consistent difference between the refinement levels; however, remarkable differences can appear in individual adjustments (Table XVI); and (9.) parameter set n ("physical set") produced the best results with non-refined data. T A B L E XVI Examples o f t h e effect of a-priori d a t a refinement, on accuracy. C o m p u t e d in Helsinki Data set

A2

A3

J2

J1

Control version

Parameter set

I m p r o v e m e n t s (%)

Difference between 2 and 1

R e f i n e m e n t 12

Refinement 2s

~txy

~xy

~z

~z

~xy

~z

~1

a b

4 1

25 19

7 -44

40 48

3 -45

15 29

B2

a b

0 -5

-5 45

-10 -71

14 8

-10 66

19 ....37

B3

a b

14 21

-12 39

25 34

-23 -64

11 13

-11 -103

B1

a b

40 42

54 51

42 40

58 67

2 -2

4 16

B2

a b

40 40

38 36

40 38

42 36

0 -2

4 0

B3

a b

19 19

6 25

22 25

6 6

3 6

0 -19

B1

2 b

6 8

0 -10

24

38

18

38

B2

a b

27 27

17 10

33 18

29 7

6 -9

12 -3

B3

a b

16 13

12 1

18 5

19 -II

2 -8

7 -12

B1

a b

40 37

36 13

37 30

34 0

-.3 ~7

-2 -18

B2

a b

40 35

44 22

37 33

38 15

-3 -2

-6 -7

B3

a b

24 18

27 9

29 24

32 23

5 6

5 14

z Compared with the resp, reference adjustment. 2 R e f i n e m e n t 1: as in reference adjustulent. 3 R e f i n e ~ e n t ~: 4-parametric transformation, no a-priori ~orrections.

~4

Side overlap Side overlap proved to be the most effective factor affecting the efficiency of self calibration. With 60% side overlap the compensation of systematic errors was about twice as efficient as wi'.th 20% aide overlap (examples can be found in Table XI). Moreover, the variations of the results were much l~ger with 20% side overlap. In the J~mijii~i blocks this phenomenon was accentuated obviously by the shortage of tie points (failure in navigation), but the same phenomenon appeared also in the Willunga blocks, which are geometrically very regular (five tie points per photo in the aide-overlapping zone). Single versus double (cross-fltghO block In accordance with expectations, the accuracy improvements obtained by self calibration in double (cross-flight) bloc[~ were clearly smaller than in single blocks (Table)[VII). Naturally, this follows from the fact that a great part of the systematic errors has already been compensated due to the flight arrangement (cf. reference adjustments without any additional parameters). E.g., in the case of the bl[ocks appearing in :['able XVII, the accuracy is better in the, double block by about 50% in planimetry and 60% in height than in the respective single blocks. TABLE ZVII Comparison of two single blocks and a cross-flight block. Computed in Aalborg Data set

Flight direct,

Control version

Reference adj.

~qelf calibration

Improvement

E1

t

F1

~

El+F1

,--t

Bi B4 B3 B1 B4 B3 B1 B4 B3

8.1 7.8 3.7 5.5 5.6 3.6 3.2 3.3 2.5

4.7 4.8 3.2 3.1 3.0 2.7 2.4 2.4 2.0

42 38 14 44 46 25 25 27 20

151 14,4 8.2 14.2 1{).8 7.5 5.9 5.1 5.1

94 10.3 7.9 10.5 8.3 5.7 5.6 5.2 4.0

(%)

38 28 4 26 23 24 5 =2 28

Con trol point pattern On the basis of the results achieved by the WG, the dependence of compensation mid the resulting accuracy on the control pattern can be expressed ~s follows: (a) In blocks with 60% side overlap, the accuracy in planimetry is only little dependent on the :ontrol pattern, that is, the weaker the control, the lm"ger the accuracy improvement obtained by self calibration. With 20% side overlap, compensation is still more e:~f,,v~.i~,ein sparse block~: but is not capable of making the final accuracy equal to ~fi]e accura,2y of dense blocks.

35

(b) In height, accuracy improvements were 25--50% in sparsely or moderately corJtrolled blocks (e,g., B1, B2, B4, and B5) and 15--20% in heavily controlled blocks (e.g., B3, B6). In other words, self calibration levelled ~ e a c c ~ y differences somewhat, but, contrary to planimetry, the final accuracy was still dependent on the con~=o~ pattern.

4.3. Test ~ l d calibration In all, the results of appr. 120 adjustments were available for evaluating the efficiency of test field calibration. They all originate from Bonn and Munich. Regarding calibration procedures, it is worth noticing that in both institutes the data used for test field calibration have been refi~.ad ~s in reference adjustment: On the contrary, the procedures differ from each other in that in Bonn significance testing was not applied, while in Munich the one-dimensional t.test (significance level 95%) was lpplied in including the parameters in the extended model. Considering all the results, the accuracy improvements were on an average 20--25% in planimet~ry and 15% in height. Although, based on a small sample, the variation in different blocks seems to meet with expectations: test field calibration manages especially well in poorly or moderately controlled blocks (Table XVIII). There are only slight differences in the performances of the different param. eter sets used in this study (Table XIX). Somewhat surprisingly, the application of test field photognphy at scale 1:8000 seemed to produce slightly better results (especially in height) than the application of test field photography at scale 1: 4000, which is also the scale of block photography. If this behaviour can be interpreted s~ evidence of a minor effect of the scale (within a reasonable range) on the successful performance of test field calibration, it implies greater freedom in the use of test field calibration. A comparison of the results of the tests achieved, by varying the number of the test field points used for calibration, indicates that there are only insignif TABLE X V l l l The performance of test field calibration in blocks of different typea estimated from the results of test field celibration performed by the p a r t k i p a n t s of WG HI/3 Control

Side overlap 20%

Side overlap 60%

Accuracy obtai ~ed (# m)

Improvement s (%)

Accuracy obtained

Improvement j (%)

P xy

~ xy

~ xy

Pz

~ xy

Pz 15--30

Pz

S~z

--

--

--

--

3--4

6--8

15--25

medium

3.5

7--8

40--46

10-20

--

--

--

dense

3--3.5

6--6.5

20

15

sparse

i Compared with the resp, refermce adjustment.

2.5--3

4.5-6

10--20

5--15

~6 T A B L E XIX Comparlt,~,n o ! t h e p e d o r m a n e e o f t h e d i f f e r e n t p w a m e t e ~ m r 8 i n t e s t f i e l d ~alSbzaticm. Ckdibration

paramete~:~ have been dotemlined from et~ss-flJlibt test strips K1 + K2 (1: 4000) and L I + L 2 (1: 8000) and utilized in the block ~Uuslment of data set F1 with the control Be. 8ilinlf~a~e teetin8 or w e i g h t i ~ have n o t b e e n a p p U e d . C o m p u t e d i n B o n n . . . . .

Pmmmoter set

No. o f teat field points

.

,

, , ,

RMSI~//~m)

,

.,.

•

,

,,

,

~

,,

,

,

,.,

- -

Scale o f t h e t e s t fliSht 1 : 8 0 0 0

Scale o f t h e t e s t flight 1:4000 ~0 ~m)

,

Impr. ~ (~)

~o

RMSBOan) lmpr.t (~)

Otm) /~z

#xy

~z

25 64 180/130

3.2 3.2 3.g

3.5 S.4 3.3

8.1 8.1 7.8

44 46 47

9 9 12

~.3 8.S 3.S

8.5 3.6 8.5

6.8 6.9 6.7

44 42 44

24 22 26

25 64 1801130

4.2 3,1 3.1

4.3 3.5 3.3

14.9 8,7 8,4

31 44 47

-67 2 6

3.2 ~!.2 3,1

3,6 3,8 3.S

8.0 7.9 7,8

4Z 39 89

10 11 12

25 64 180tt30

3.1 3.1 3.1

3,4 3.3 3,3

7.7 7.7 7.8

46 47 47

13 13 12

3.3 33 3.2

~.5 3,6 ~,4

~,0 7,1 ~.$

44 42 45

21 20 Z4

25 ~4 1801130

3.b 3.4 3.4

3.6 •6 $.5

8.0 7.9 7.7

42 42 44

10 11 13

3.3 3.3 3,3

3.5 3.6 3.5

7.1 ?.2 6.9

44 42 44

20 19 22

C o m p ~ v d w i t h t h e re~p. r,sfet~ne~ ~ J u ~ t m e n t .

icant di!~ferences between the three cases applied (Tables IX, XX and XXI). This is a very favou~ble finding, considering the economic aspect of calibration. Table XXII gives some evidence of a possible loss of information that may occur in connection with test field calibration, due to the fact that the circumstances of test field photography and of b]oc~ photogral~hy are not identical.

T A B L E XX D e p e n d e n c e of t h e e f f i c i e n c y o f test field e&Ubration o n t h e scale of te~t strip p h o t o g r a p h y , t h e ~to. of te~t field point~ u s e d f o r cal!ibration a n d t h e c o n t r o l o f t h e b h ~ k . D a t a set DS, o r t h o g o n a l ~ m ' ~ m e t e r ~et b (sJgn~f|canec level 95% a p p l i e d ) . C o m p u t e d in M u r d e h Data used for e~l|hr,

No. o~ tem~ ~i$1(~

C o n t r c 4 B3 , d e n s e )

C o n t r o l B1 (spmr~) so ~m)

PoMSE Otto)

I m p r , I (%)

tZxy

~

~xy

#z

so (~m)

RMSE (.urn) Impr~ 2 (%) ~x.v

#z

~xy

/Zz

LI*L2 (1 : 8 0 0 0 )

25 64 130

3.9 3.9 3.8

2.4 2.4 2.4

6.0 5~8 5,8

27 27 27

17 19 19

3.9 3.9 3.9

2,4 2.4 2.3

4.5 4,5 4.5

14 14 18

10 10 10

K1~2 ~]: 4 0 0 9 )

25 64 180

4.1 4.1 4.2

2.8 2.9 2.9

6,~ 6,2 6.2

15 12 12

14 14 14

4.1 .~.2 4.?

2.4 ~.~ 2.6

5.0 5.0 5.0

14 7 7

0 0 0

ComD,~red w i t h ~,he rc~p. ~ f e r e n e ~ adjustraertt.

37 TABLE XXI Dependence of ~ ~ e n e ~ of test field calibration on the scale of test strip photography, the no. of test field points used for calibration and the c.c.n-~Po.!of the block. Data set CS, orthogonal parameter set b (significance level 95% ~pplted). Computed in Munich Data u d for calibr, (scale)

No0 of test field points

Control B1 ( a p U ) ao

Control B3 ( d e r ~ )

RMSE (pro) Impr,s (%) Pxy

Pz

~xy

/~z

so

RMSE (#m) Impr.l (%) #xy

#z

#xy

,~z

LI+L2 (1: 8000)

25 64 LSO

4.3 4.3 4.2

~.S ¢.4 4.3

8.2 8.0 8.2

17 15 17

29 30 29

4.4 4.4 4.4

3.1 3.3 3.1

5.5 5.~ 5.5

21 15 21

18 18 18

KI+K2 (1: 4 0 0 0 )

2b 64 IS0

4.4 4,3 4.3

4.2 4.1 4.1

8.0 7.7 7.2

19 21 21

30 3S 37

4.5 4.4 4.4

3.0 3.0 3.0

5.~ 6.0 ~.7

23 23 23

15 10 .t 5

l Compared with the reap. reference adjustment.

TAB L E XXII C o m p a r i s o n o f t h e i m p r o v e m e n t s (in percentages with respect to resp. reference adjustm e n t ) o b t a i n e d b y tw o d i f f e r e n t test field calibration procedures. Data set F1, c o n t r o l B5. C o m p u t e d in B o n n Parmneter set

I

a f d

Procedure A z

Procedure B2

#xy

~

#xy

Pz

44 42 44 44

24 10 21 20

55 55 55 51

~0 47 49 53

' Calibration p a r a m e t e r s d e t e r m i n e d f r o m the separate test field flight (data set L I + L2, 25 test field p o i n t s used). =Calibration p a r a m e t e r s d e t e r m i n e d b y using 3 p h o t o s p i c k e d from the bloc k (ffi "ideal case of test field c a l i b r a t i o n " ) .

4.4. Component calibration Considering the number of results, component calibration was the method which was of least interest to the participants. Some results can, however, be given concerning: (a) the correction of film distortion by means of a reseau; (b) image coordinate transformations; and (c) the correction of radial distortion sectorwise. Only the first subject has been properly treated, as for the others, the results presented serve only a~ an example. Correction of film distortion by means of a reseau In Hannover, all Willunga blocks were computed after refining the data by spline interpolation. Corrections for photo coordinates were derived from

B1 B3

B1 B3

A1

A3

3.7 2.9

5.8 3.8 17.7 5.1

32.0 8.4 3.4 2_9

5.4 3.7 10.4 4.4

14.3 6.9

~z

/~xy

~xy

/~z

12 [iarameters and 16 crosses 2

6 parameters and 25 crosses ~

Evenly distributed~ 2 L~catmg on the image borders. s Compared witch the ~ - ~ . ref. a d j u ~ ~ent.

Control

Data set

3.4 2.8

5.3 3.7

~xy

10.2 4.2

12.0 6.6

~z

24 15

19 10

~xy

10 7

6 13

~z

6 and 25

31 15

25 12

~xy

47 20

58 29

~Zz

1 2 a n d 16

I m p r o v e m e n t 3 (%)

31 18

26 12

~xy

48 24

65 3~

~Z

1 2 a m i 25

coo¢ :dinate transformation. WiUunga r e ~ a u data.

12 parameters and 25 c r o s ~ s ~

Comparison o f the results of bundle adjustments after different i m ~ C o m p u t e d in H e ~ n k i

TABLE XXHI

39

the residual errors after affin~ (6 parameters) transformation o n 2 5 reseau croNeti.

The r]~ults reported show that there are only ~ i g n i f i c a n t differences (some per cents) in t h e accuracies aclu'eved with and without the reseau corrections (see ~ JacObsen, 1980). ~

Co,~,pen~tion o f film distortion by image coordinate transforr~ation Tables XXIH and XXIV prc~ent the results of a comparison of affine (6 parameters) ~ s f o r m a t i o n and o f a 1 2 - p ~ e t r i c transformation given by the formulas (computation in Helsinki): Xp = a l + a:~X + ct3Y + G4xY + asY 2 + a~.Ty 2

Yp = bl + b2Y + bsx + b , x y + bsx ~ + b6yx 2. Two observations can be made from the results: (1) 12.parametric transformation produces very good results with the Willunga data, while it is fairly inefficient with the Jiimijiirvi data. (2) The use of 25 reseau crosses evenly distributed over the image area does not give better results than the use of 16 boarder crosses.

TABLE XXIV Comparison of the results of bundle adjustments after dlffere~t image coordinate transformations. Jiimij~rvi/MRB data. Computed in Helsinki Data s~t

J1 J3

Control

B1 B3 B1 B3

6 parameters and 20 flduciais

12 parameters and 20 fidueials

Improvemvnt ~ {%) 6 and 20

12 and 20

Pxy

Pz

/'~xy

PZ

Pxy

#z

PXy

P'z

4.2 3.4 3.1 2.8

11.3 9.4 10.2 6.2

3.8 3.6 3.0 2.8

15.0 8.8 10.5 6.3

0 11 28 18

0 -3 2 6

10 5 30 18

33 3 -1 5

I Compared with the resp. reference adjustment.

Correction o f r#dial distortion sectorwi~e With the same data ~s in the previous case, a series of adjustments, where radial distortion was corrected sectorwise based on laborato~/calibration data, was carried out in Helsinki. The results showed no accuracy improvement as compexed with the adjustments where mean radial dhtortion correct!on was applied.

40 5. CONCLUSIONS

The relatively small number of results using the different methods does not justify the establishment of recommendations for Computation. Some facts, nevertheless, can be rather clearly and reliably seen hz the results achieved by the WG. It is believed that, e.g. the following findingt~ are worth consideration: (a) The calibration methods applied improw=d the accuracy of aerial triangulation on an average by 20%.The results varied, however, considerably depending on the calibration method, the calib:~ztiov~ procedure, the project p~ameters, and, of course, the data concerned (b) Generally, self calibration proved to pro, luce better results than test field calibration, but the differences were, however, practically negligible. (c) No single parameter set was found to be tmper~ior to the others. This refers both to self calibration and to test field c~ibration. (d) In order to secure reliable and accurate results, proper attention should be paid to the accomplishment of self calibration in poorly controlled blocks (especially, side overlap tu:~ed out to be a critical f~Lctor). Unfortunately, this study does not provide any r e l e v ~ t information regarding the application of significance '~esting and the treatment of con'elations. On the o~her hm~d~ the favourable effect of weighting was quite obvious. Further, it is alamo worth noticing that the introduction of stripinvariant- instead of blockinvariant -- additional parameters was not~ successful. (e) Regarding test field calibration, the most important finding was the independence of the results of the number of test field points used for calibration (the number of points varied from 25 to 180 in this study), which is attractive from the economical point of view. Finally, it is felt that the matters which still remained inadequately studied in this context and to which efforts should be directed, are, above all, the significance testing of additional p~ametert~ and the consideration of correlations both ia self calibration and in test field calibration. Furthermore, concerning self calibration, it is suggested that further studies should be made an the dependence of compensation on side overlap and the distribution and numbe~ of tie points. In such investigations simulati~on techniques m'e obviously both applicable and flexible. ACKNOWLEDGEMENTS

The author wishes to thank all participants of ~he WG for their enthusiastic interest in the study concerned. My special thanks ¢~e due to the South Australian Lands Department and the Finnish National Board of Survey. Their roles in getting re~arch materia~ were decisive. Further~ ! thank ~|l those organizations which were not able to participate in 1;he WG-studies but provided large support in its various phases. Above all I w ~ t to mention the Carl Zeiss factory, Jena which provided the camera f~r tes~; photography~ in particular, I wish to thank Messrs. Keijo Inkil~i and Jan Heikkil~: for helping me during the whole project, especially in analyzing the ~'e~ults and compiling this final report.

41

APPENDIX A. Parameter sets in t h e studies of the WG III/3 Parameter set a proposed by B r o v m (1976): dx = a~x + a2y + a~xy + a4y ~ + asx~y + a6xy= + a~x~y ~ + x

~.

•

X

X

[al3(X 2 - y : ) + at4x2y 2 + a]s(X 4 - y 4 ) ] +

+ X [alt;(X2 + y2) + at,;(z2 + y2)2 + ats(X2 + 3/2)3] dy

= a s x y + a ~ x 2 + aloxaY + a t l x Y :~ + a~ax2y 2 + y--- X .

× ~,~3(x2 _y~) +

a~4x~Y2 + a~,s(X4

+ y [ a l 6 ( x 2 + y2) + Parameter set b dx

dy

alT(x2 +

2B2/3)y +

4B2/3) +

ats(X 2 +

y2)3]

+ bs(z- - 2B=/3)y +

b4xY + bs(Y 2 -

2B2/3) +

bTx(x 2 -

2B2/3) +

2B2/3)

bll(X 2-

= - blY + b2x + b3xy -

P a r a m e t e r se~

y2)2 +

_y4)] +

proposed by Ebner (1976)"

= blx + b2Y - b3(2x 2 bg(x2 -

c

b4(2Y = - 4B2/3) + blox(Y 2 -

2B=/3) +

b6(x 2 bl2(x 2 -

2B=/3) 2B=/3)(y 2 - 2B2/3)

c proposed by El-Hakim and Faig (1977)"

dx = a~x + a2y + q X r

Y dy = -a~y + a2x + q-r, where

q - a3rcos~ + a4rsin?, + asr 2 + a6r2cos2)~ + aTr2sin2~ + asr3cos), + a9r3sin;~ + + a~or3cos3k + a~r3sin3k r = x/~X2+Y -~' and )~ -'* arctan -Yx

Parameter

set d proposed by GRin (1976):

dx = aly ÷ ,~ x y 2 + a 3 x 2 y dy = bly 4. b 2 x y + b 3 x y 2 + b 4 x 2 y Parameter s e t e

proposed by GRin (1976)"

dx = aly + a.~y 2 + a 3 x y + a 4 x y 2 + a s x 2 y dy = blY

+ b2xy + b 3 x y

2 + b4x 2 + bsx2y

42

P a r a m e t e r 8e$ t p r o p o s e d b y Griin ( 1 9 7 6 ) : d x = a t y + a 2 x y + a3xY 2 + a4x2Y + asY 2 + a6z2Y 2 d y =: b l Y + b=xy + b 3 x y a + b 4 x 2 y + b s x "~+ b 6 x l Y 2 P a r a m e t e r set g p r o p o s e d by C,riin ( 1 9 7 6 ) : d x = a ~ y + a 2 y 2 + a 3 y 3 + a4a'y + a s x Y 2 + a 6 x a Y + a ~ x 3

dy = -- b~y + bay ~ + b ~ x y ÷ ~ x y " + b s x ~ + b~x~y + b~x ~ Pa:~:ne$er set h p r o p o s e d b y G riin ( 1 9 7 8 ) : d x = a~,ax + a~,y + a::zxy + a ~ l - b~z ~77 k + a t 4 x p + a=~yk • a ~ x l + c4~yq + + a, :c + a ~ x y p

+ asskl + a4~xyq + as~s + a~syr + a~4xlp + a4~ykq +

+ as~XS + a~sir + a 4 4 x y p c f + as,.+ks + a4syqr ÷ a s 4 X p S + assrs 10 ([Y ffi -- at~Y + aa~x - a a z ~ I + bt~k + b~zxy + b t 4 x p + b ~ y k + b ~ x l + b+tyo. + + b~sr + b~4xyp + bsskl + b4~xyq + bs~s + b~syr + b~4xlp + b4~ykq +

k

+ bs~xs + b4syqr + bs~x$,s + bssr~l, where b ~ l = y ~ - -b- ~ = x : - -2-; ~ 17 b 2 y~ 17 b ~ x . ~ ( x ~ _ 31 b ~ ) + 2 ;p=x "'~ ; q= -20 ; r= , [§.

++++.,-fo +"

+""

Paramet~er sets i a n d j (i includes the first 16 and j all 20 p a r a m e t e r s ) p r o p o s e d by Jacobsen ( 1 9 8 0 ) :

dx -" p ~x cos ( 2arct~an y )+ p 2 x s i n ( 2arctar, f- ) + p s x c o s (arctan Y-- ) + X

X

X

+ p 4 x x i n ( a r c t a n Y ) + p s y r c o s ( a r c t a n Y--) + p + y r s i n ( e x c t a n Y-- )+ '

X

X

+ pTx(r 2 - A) + psx(r ~-Br-c) + plox(r ~ - Hr 7 -...-Nr-

X

+ p , x ( r 4 - D r "~--Er 2 - F r - G )

+

P) + p l t x c , m ( 4 a r c t a n Y--) + p l 2 x s i n ( 4 a r c t a n Y--) + X

X

+ p i s x ( r ~ - 1 2 1 0 0 ) c o s ( 2 a r c t a n ~Y )+ ,o 1 4 x ( r 2 - 1 2 1 0 0 ) s i n ( 2 a r c t a n ~Y )+ + plsx(r 2 -

1 2 1 0 0 ) c o s ( 4 a r c t a n y ) + p l + x ( r 2 - 12~ 0 0 ) s i n (4archon Y-- ) + X

X

+ PtTX + P~,sY + p t g x y ' r Y ~y =#,,,ycos(2,~ct~o~n -) + p2ysin (2arctan y ) + psyco, s(atct~ -Y- )+ X

X

X

+ p4ysh~(arc, t,an ~ ) + psXrCOsCarctan ~ ) + p+xrsint, arct~m Y--) + X

X

X

43

+ p~y(r = - A ) + p s y ( r = - B r - - ¢ ) + p g y ( r 4 - D r S - E r = - F r - G ) + ploy (rS-Hr~-...-Nr-P)

+

+ p t l y c o s (4arctan Y--) + pt2ys:in (4arctan Y.) + X

X

Y ) + p l 4 y ( r 2 - 1 2 1 0 0 ) s i n ( 2 a r c t a n ~y )+ + Pt3Y (r 2 - 1 2 1 0 0 ) c o s ( 2arci~n ~+ p ~ y ( r 2 - 1 2 1 0 0 ) c o s (4arctan Y--) + pt6y (r ~- 12100)sin (4arctan y ) ÷ X

X

+ p ~ Y + P~sX + p~0xy Parameter set k proposed by KSlbl and modified by Jubl (1979): dx = as ~x ( r 3 - r l r = o ) + a 4 x ( s i n rrno)a + a s r xS i n ( _~_o)÷ r , = ' , y- r ( a 6 c ° s a +aTsina +

+ a s c o s 2 a + agsin2a) 2

dy = a t x +a2Y + a 3 ~ ( r a - r / r ~ ) + a 4 y ( s i n r ~ ) +as Ysin(2r~,)+ ro

+

r

ro

r I"ss. ~ (a,~co~ + aTsin~ + ascos~ + agsing.~), r

where: a

=

arctan Y-X

r o = a given constant (radial distance, where radial distortion is wanted to be zero for the second time) Parameter set I proposed by Mauelshagen (1.977)' dx = a4xy + asy 2 + a6x 3 + aTx2y + a~xy 2 + agy 3

dy = b l x + b2y + b3x 2 + b4xy + b6x 3 + bTx2y + b s x y 2 + bgy 3 Parameter set m proposed by ~chut ~1978)" d x = c 3 x Y + c s Y 2 + cTx2Y + c g x y 2 + c ~ x 2 y 2 + CI3X 3 dy

= c l Y + c 2 x + c 4 x 2 + c 6 x y + c ~ x 2 Y + C~oXY 2 + c i 2 x 2 Y 2 + c~4Y 3

Parameter set n (cf. text): dX

=

b l x + b~y + b 3 x r 2 ( 1 - r o l r ) + b 4 x r 4 ( 1 - r o / r ) + b s x r 6 ( 1 - r o / r ) + + b ~ 2 x y + b~(r 2 + 2x 2)

dy = -- bty + b2x + b 3 y r 2 ( 1 - r o / r ) + b 4 y r 4 ( 1 - r o / r ) + b s x r 6 ( 1 - r o / r ) + + b6(r 2 + 2y 2) + b~ 2xy, w~ere r o is a constant (first radial distance, where radial distortion is wanted to be zero).

d4 REFERENCES !~own, D.C., 1976. The bundle a d j u s t m e n t - Progress and prospects. Invited Paper to the Xlllth Con~q~emof ~the ISP, Commission III, Helsinki. Ebner, H., 1976. Solf-calib~ating block adjustment. Invited Paper to the XIIIth Congress of the ISP, Connnission HI, Helsinki. ~l-Hakim, S.F., ~nd Faig, W., 1977. Compensation of systematic image errors using spherical harmoni¢~, lh'.~)ceedinp of the American Society of Photogrammetry, Papers from the 1977 Fa~l Technica| Meeting, pp. 492--499. Grtin, A., 1976. Die sh~ultane Kompensatio,~ system~tischer Fehler mit dem Miinchener Biindelprol~amm MBOP. Presented Pa~er to the XIIith Congress of the IS]P, Commission Ill, Hel~nki. Griin, A.. 19~8. Experiences with self-calibrating bundle adjustment. Presented Paper to the ACS~I..,~SP Cow~ention, Washington, D.C. Jacobu;n, K., 1980. Ate,erupt at obtaininl~ the best possible accuracy in bundle block adjustl~mt. Presented Paper to the XIVth Congress of the ISP, Commission Ill, Hambm3. J~;hl, J., ~(.i,79. Results from J~/mij~rvi. Contributions t~ the ISP WG III/3 Seminar, Aalborg May 1~,....18, 1979, pp., 39--52. M~,uelshag,~n, L., 1977. Teiikalibrierung emes photogrammetrischen Systema mit variabler Passpuwktanordnung und unterschiedlichen d~,termiuistischen An~itzen (Dks.), DGK, Reihe C, Heft t~]r. 236. Miinchen. Schut, G.Ho, 1978. Selection of additional pararneterl~ for bundke adjustment. Presented st t;he ,Symposium of Commission III of the I;~P, Moscow.