EXTERIOR ORIENTATION IN PHOTOGRAMMETRY 553

the line of intersection between the photographic and Survey planes. The positiveY-axis points toward the North.

The rotation operations and matrix multiplications then take place as indicatedin Figure 6, and lead to the Church orientation matrix.

As stated earlier, the Church system is based directly upon the standard Eulerianangles. Euler's angles are three angles chosen to fix the directions of a new set ofrectangular space coordinate axes (photo) with reference to an old set (Survey). Theyare the angles between the old and new Z-axis, 8, (corresponds to t), the angle be­tween the new x-axis and the intersection of the new xy-planewith the old xy-plane,..p, (corresponds to s), and the angle between this intersection and the old x-axis, ¢'(corresponds to a-180° (6) Figure 8 illustrates this relationship.

A major disadvantage of the Church system is that it breaks down for the idealaerial photograph, the true vertical, the primary purpose for which it was developed.When there is no tilt, the two planes are either parallel or coincident, and there is noline of intersection (or principal line); thus the angles of swing and azimuth areundefined.

Use of Photogrammetry zn Architecture and OtherCivil Engineering Construction

M. PLOTN ICK,

Minerva Str. 29, Zurich 7, Switzerland

INTRODUCTIONItRCHITECTURAL Photogrammetry has de­

n veloped into a field of considerable tech­nical and professional importance, during itsuse since \iVorld \iVar II. Sweden, France, TheNetherlands and Switzerland have found itadvisable to record their historical Archi tec­ture by Photogrammetry. In the U.S.A. de­velopments in this field have progressed atOhio State University's School of Architec­ture and Landscape Architecture, combinedwith the Institute of Photogrammetry,Geodesy, and Cartography. Professor BertilHallert, Director of the PhotogrammetricInstitute of the Royal Swedish Institute ofTechnology at Stockholm, published a paperon the extensive work done there in determin­ing accuracy and the theory of error, in archi­tectural and other terrestrial photogram­metry.

Photographic surveying of the historicbuildings has been carried out systematicallyin Belgium during the years 1955/56 and apublication of "Photographic Surveying ofHistoric buildings in Belgium" was issued bythe director of the "Service de Topographieet de Photogrammetrie du Ministere desTravaux Publics," Ing. F.].G. Cattelain &Ing. P. Vermeir.

A demonstration of the practical uses of themethod of stereophotogram metry as appliedto Architecture/Archaeology is given below.It has also proved its worth in city planning,mining development and other civil engineer­ing work, where the projects are investigatedand studied from elevation plans.

This paper is based on a project in archi­tectural photogrammetry at the Swiss Fed­eral Institute of Technology, in which theWILD photo theodolite and WILD auto­graph A-5 were used. However this proceduredoes not need specific instruments but can becarried out with any standard existing instru­men ts. Presen ted in this paper are some si m­pIe concepts of architectural photogram­metry, which may serve as an aid in explain­ing the relation of the subject to otherbranches of civil engineering.

The project under review involved thepreparation of elevation plans at a scale of1: 100 of 50 ancient buildings within the oldcity of Lucerne, Switzerland. Although mod­ern buildings are being constructed in thispart of the town, too, the town-planning officeaims at retaining as much as is possible, thecharacter of the "old ci ty." The elevationplans of the buildings to be demolished andof the neighboring houses will be of great

554 PHOTOGRAMMETRIC ENGINEERING

assistance in this respect. The classicalmethod involves far greater expendituresince scaffolding is necessary.

Equipment for taking photographs spe­cially suitable for the task has been createdand perfected by "Officine Galileo" Florence,under technical control of M. E. Santoni.

GENERAL PRINCIPLES

As a first preliminary step one must decideon the scale to be used in the stereoplotter.This depends on the scale of plotting, the ob­ject distance, and the dimensions of the ap­paratus. In terrestrial photogrammetry thedistance between the camera stations and thepoints to be plotted is introduced along theZ axis. In the Autograph A-5, the range of dis­tance is from 114 mm. to 500 mm. The ma­chine scale is so chosen that the minimumand maximum distances are within theselimits, bearing in mind the transmission ratiofrom the stereoplotter to the drawing table.

At each of the camera stations 0' and 0',photographs usually are taken horizontally.The distance between the two stations, theso-called base b, is measured (Figure 1). Itmust be selected in relation to the object dis­tance. (Base b is about a 10th of the objectdistance.) Furthermore, the base must be par­allel to the object plane, in order to get thetrue elevation plane.

Any point P on the surface of this over­lapping range will thus be represented bypoints P' and P" respectively. In the plottinginstru men t, the posi tions of each surfacepoint P can be mapped at a reduced scalefrom its images P' and plI, provided that boththe interior and exterior orientations of the

FIG. 1

cameras can be reproduced. The interiororientation includes the principal distanceand the position of the photoplane relative tothe projection-center. The exterior orienta­tion corresponds to the absolute posi tion ofthe cameras in space, in the given system.

In terrestrial photogrammetry, the outerorientation of the camera (phototheodolite)relative to the base and the horizontal, aswell as the base length and the heights of thetwo stations, are known. (See Tables I, II.)Thus all orientation can be set in the stereo­plotter right at the beginning of the operation.

Photographs are normally taken at rightangles to the base: the computed base reducedto the machine scale is set as bx. Should therebe any difference in height between the sta­tions, it is introduced-reduced to scale asby. When the photographs are inclined rela­tive to the horizontal, the angle of tilt, as setin the phototheodolite, is introduced to the

MODEL "" AASE ~L-UR b:c b,,' bl/' hz' bz" If' """ w' uJ" 'It' ?til

1 "' -~ .'1 ....0 n ~n nnn nfWYln nnnN1n.~~~=-~~,

O,,"~O 00000o lOOO 10

• " n~ ~~ ~"""" 082110 000000 lOOO Xl. '" + 2 000 000000 000000 00000 100000 0820 M"~O nnnnnnIIVYl '"

~..-..t::.. +1. KlOOO 10000 I00000 , 00000 OR20, 0"" \0 00000o lOQ() 10

WL..J: WV\n IOOnn ,n"""n ,nnnnn no,,,, no,non nnnnnn IIVYl

12 '" 2.";0 - 0 o >nnnn 10000 nil""" 1nIIMn nA~n, (\A,n~n nnnllrV\ IIVYl.... '" 2 ,<0 """'" )000 100000 M,non o",oao 000000 onnnnalq " 2 + '0000 'noo 0"'000 onnnnn nnnrIIY>

'0 '" , MCIOOC .nnn no,non n"""nn 1IrV\NY>

" • - nooncc 'non "",nan nnnntVl nntVVY>

f" 2. + I~ 8.40 0 '000 0"'000 MnIVV\ nnntwV'o

'" , + ''''''' OR' 101'1 nnnnnn nnt\/'lOll.' 2 + '000 OR" ~O 000000 000000

" , 1001 lnoOOO M)OOO OR,ooO nnnOllO nnooao,a I

'''0 rlOOO '00000 100000 I'll! "'nil ""2t .0 0ClllCl0l'l 0Mtl00

10.,

2_860 "+ 100000 .00000 10000I\ ""'000 OR" '0 nnnono 0Il0CI00a ,.,,~O + 20 00000o KlOOOO 00000 00000 100000 100000 1 ..00000 OOOOOC, ,

o.a?< .28 '000 • n.n<n 000000 • 00000 t 00000 ORRnoo 1'1""100 '1'100000 000000., '" a.a?< a 1Q_QO non O/l() nonnno noMnn 1Mnon , MOno OA,Ono 1'1"'7'0 nnnNY> nnnnnn~. 0 a_a·" a la.an lXlO aoo, 00000o nooooo '00000 ,naOM , MOno 1MnM nnnnoo nnnono., " '_<60 - <1_20 ~(L20 NY> nnnnnn 000000 '00000 t 00000 M,OOO M'~"O •nooooc nnnnnn2211.1lO " ~ ,<_,00 ~ """no '0 loa. 2'1 1 07<~< nonnno ,nonM "QS;nn n"'nnn nFl,,, nnnn.. """"""

TABLE 1

MODEL SCALE 1: 50 F/L=165.02 mm.

PHOTOGRAMMETRY IN ARCHITECTURE AND CONSTRUCTION 555

')('w"w'.ASI ilL-Hit bx bll' bll" bz' bz· '/" Cf"!V'+. • ~on_'_ ... 0_ 0 GM M'Mn .nu~, I.IVVVV' ~ ""''''0 nnnnnn nnnnnn

HODEL fII'

2 ,. • ....0 -. n ,. non nnnnnn ~ I.IVVWV' 'N 000 ""'A' nnnnnn rvvv>nn

~.~ • un 0 I'L 000 ,oo,nn 00071> t MMr "', non n'" t t>nnnnn nnnnnn• '" , _, .to .. n 000 oooonn 1>000<> • n""nr 'no "''' no"""" nnnnnll< '" • ton .. 'jW """ ~QQQO _nno"", ,nnnnil "" nnn MOl nononn nonnnn< 'Y..o -, ton Olll'l 002591 _1-07.... ,'MOM 00000 082000 08'0 a 000000 00000: .;;; • 'on _ 000 nO"""" nnnt'II'lo • ""OM ,nnnno OR,onn OR2'" 0 nnMrO Mt'IOt'IO

• ,..n _ a 000 6922 tAQO 10000l' \00000 082000 082020 ooooooriooooo.. '" -~ ,on + c 000 000000 """""'" nn nAonnn n... on nnnnno nnnoM

.' - 1 -" a 000 0000()( 0000001. nnnN • nrvvv' n. 'M' 011 ,oc 100000., ':: .. o. 0 000 OOOOQ( Manne 1.ntVVY' <n.QQlll!~f-~08~'0lll"f0C_-""08"-U:",!-~lo/!.800",+--,,0M1lnfVVV'.M.1•.. - -0 0 oon nonOCY nn<Vlt>( 1000'" 10000 rIA 000 08: <Xl nooood

t--'~"~N.:~+~~0~0~+=-~_+-~L..J.;lI-=..nQ..)iQj-J!001Q04~tnQ)9~' OQO,,, I • nnntY -.r;;;;:;;;r nA 'rvv nA' "'" nnnoN• Q '" 0.. "0 O. oon onoon, nnnnO< I • nnnn, ,nnno 08 000 08: 0000 00

•• 'lYle. _ .. c on _n MO OnoM' ,. HfII' ,nnn, -,-r;fV)M oeifYV' 08206 000000 000

'2· • _• o. -0 \ 000 0000 . OOOnnnl \ 000 onr -'OnOO 1000'\( 000000 ooonor~, -"l.... _. on' _0 non "". 09.2A.6S Innn, .nM n_Mr OAA"'~' nMM'

n " I. \ ...,. ~ .\ 0 2 000 0000 o;:;;:;;v:;;r1""" 0"""" OR.nor MOl" nnt'InNI nnnnfII

TABLE 2

MODEL SCALE 1: 100 F/L=165.02 mm.

stereoplotter on both cameras as an w rota­tion. (In our project the phototheodolite wasset up provisional1y, and the maximum angleof tilt upwards used was about 18 g.) If thephotographs are not taken at right-angles, butare swivel1ed to the base, then the two cameraaxes are paral1el to one another, turned rela­tive to the base by the horizontal angle cPo

The base can be divided into two compo­nents "bx" and "bz." According to theformula:

bx = b·cos '"

bz = b·sin '"

where cP = angle of swivel (see Figure 2).These values are of course to be reduced onthe plotting scale of machine.

The operation of plotting a model consistsin setting the dimensionally-seen floatingmark, by means of the two hand wheels, X,Yand the foot disc Z along surface lines to bemapped. In terrestrial photogrammetry, it isan advantage when the two stations of thebase (L and R) are at about the same height.Thus the maximum coverage of the model inthe vertical direction by the two exposures isachieved.

To study the area surrounding the objectto be measured by this method, it is neces­sary to first plan the number and location ofthe stations which will be fixed on the ground.However it is not necessary to establish theabsolute position of the stations, since we aredealing with relative relationships.

CHARACTERISTICS OF INSTRUMENTS

There are three common approaches tosolving engineering problems by creating ele­vations: Analytical or mathematical, graphi­cal and mechanical (i.e. with the use of aninstrument).

For carrying out the concepts previouslypresented and in actual practice, the thirdapproach has been found to be most feasibleand useful for this method. 'vVe use a first­order plotting instrument of the universaltype, which creates and measures a specialmodel and records the results. The functionalcomponents of the instrument include differ­ent types of facilities available to the photo-

.s-6)(---~

s- 6x\

FIG. 2

556 PHOTOGRAMMETRIC ENGINEERING

FIG. 3

grammetric engineer and scientist. They are:Focal-length f, swing K'K", lateral-tilt w'w",

longi tudi nal C/>' c/>".base components bxbase components by'by"base components bz'bz"and X, Y,Z. (Figure 3)

The values of all base-components can be setand read from measuring counters of whichthe smallest divisions correspond to 0, 0 Im"m.

It is possible to shift from terrestrial toaerial work by a gear change. This is usefulthrough allowing the drawing of elevations,­horizon tal sections and partial ceiling plans,-without changing the orientation of thestereopair. By means of a knob, movementbetween Yand Z can be interchanged. The Zmovement is then coupled to the hand wheeland the Y counter, the Y movement to thefoot disc and the Z coun ter.

CONTROL

We have noted how this special model canbe constructed wi th terrestrial photographs.To know the model-scale and its location in

an established reference frame work, we haveto achieve dimensional control in the model.The need for control can be illustrated bycomparison with conventional aerial survey­ing. So we have to measure at least one dis­tance in order to determine and to check thescale of the model. Another requirement is togive the heights of the two control points. Thethus-mentioned requirements, scale andheights, can be satisfied by having two pointsin the model of a known horizontal position.In order to refer the elevation in our surfaceto a standard datum, such as mean sea level,we would need the mean sea level elevation ofthe two control points.

To this point an individual model formedby two exposures has been discussed. If wehave oriented, scaled and leveled one of theindividual models, it is possible to determinethe special location and all poin ts of the sur­face from other common overlapping models.The condition of this process can be tolerateduntil our error accumulation becomes toolarge. The important point in this method isthat the outside control in every individualmodel is not necessary.

FIG. 4. A stereopair taken at right angle to the base. (Not prepared for Lise with stereoscope.)

PHOTOGRAMMETRY IN ARCHITECTURE AND CONSTRUCTION 557

"'r rr

~'"-

[ ~ ~

'DD~~DD'J'if=-1:,,=,,::,.======f:l-.J:J::======,;,,::J,,:=-.._

FIG. 5. A reconstruction of Fig. 4.

ERRORS A~D ACCURACY

All measurement systems and their instru­ments contain sources of error. Of course wenever completely eliminate all errors, but westrive to red uce the total resid ual errors un tilwe obtain the desired precision and accuracy.However, the photogrammetric engineer canreduce and correct any measurements, as wellas minute errors of the project. The accuracyof the method is therefore essentially con­cerned wi th our abili ty to construct themodel. There are many factors such as thegreat importance of inner orientation in de-

termining model errors. These errors affectthe exterior orientation as well as the positionerrors of the model in space and its deforma­tion. The accuracy of measurements fromthe photograph is largely dependent upon thecare with which the work is done. Positionerrors should be ± 0.2 mm. at all scales, pro­vided the correct base-length is selected.

A description of errors is given by Prof.Dr. lVI. Zeller in his Text Book of Photogram­metry, where he investigates these errors anddiscusses their elimination in detail.

PLOTTI:\G OF ELEVATIO:\f PLANS

The following actions apply to plottingelevation plans: selecting the model-scale, in­serting negatives, setting the optical andmechanical equipment, introduction of theorien tation elements and the base, connec­tion with drawing table, compensation ofminute errors at the time of exposure.

Selection of model scale. As in the plottingof aerial photographs, the selection of themodel-scale depends on the scale of the eleva­tion plan to be produced, as well as on theavailable gear ratios from the stereoplotterto the drawing table. The distance range ofthe model to be plotted must lie within theinstrument's ranges.

Inserting the negatives. When doing this theranges of movements of the camera tilt, etc..must be considered together with the settingpossibili ties of the optical and mechanicalparts. The model as seen in the stereoplotteris so presented to the observer that a rotationof the righ t hand-wheel to the righ t causesthe floating mark to be moved to the right inthe X direction.

Orientation elements. To reconstruct the in­terior orientation, the focal-lengths of theplotting cameras are set equal to that of thecalibrated focal-length of the phototheodolitecamera. The pictures themseh'es are so in-

FIG. 6. A stereopair taken swivelled relative to the base.

SS8 PHOTOGRAMMETRIC ENGINEERING

Fig. 7. (A) and (B) This is a demonstration ofan incomplete elevation of Fig. 6.

A

serted in the plotting cameras that the fiducialmarks of the phototheodolite camera coincidewith the corresponding marks of the pictureearners.

For reconstructing the exterior orientation,

the two plotting cameras are so placed thatthey have the same position relative to eachother at the moment of exposure at the twoground-stations. The following orientationdata or measured field survey must be set inthe stereoplotter:

1. Base length: This is the measured hori­zon tal distance between the exposurestations; it is set in the stereo-plotter asthe reduced base in the model-scale(bx).

2. Height difference between the exposurestations (HL-HR): This is the meas­ured heigh t di fference and is set as "by"in the model-scale.

3. Tilt: If the two photographic cameraswere tilted the same amount, upwards ordownwards, from the horizontal axis,the tilt angles are set in the instrumentas w rotation. Finally, set on the plottinginstrument the correct amount of wandeliminate any difference between Wi andw" where Wi and w" do not coincide ex­actly. The w rotation causes the imagesto appear rotated about the optical axesin the eyepieces. This effect can becompensated for by rotating the doveprisms.

In order to extend the surface surveyedfrom one base, additional pairs of swiveledexposures can be used. The two camera axesare then parallel to one another but swivelledrelative to the base by horizontal angle.p. Thisswivel is introduced in the Autograph bymovement of the base instead of by camerarotation. The measured base is divided into acomponent normal to the direction of ex­posure and one parallel to it and introducedas bx and bz (see Figure 2).

The swiveled exposures, however, have thedisadvantage that the elevation has to bereconstructed in accord with the true hori­zontal plane--the house front not being inthe true elevation position.

Thus additional drawing work had to bedone, so as to reconstruct to a normal preciseelevation plane.

Compensations of minute errors in the orien­tation data. \Ve use the Y, and Z gears in theplotting of the elevation plane and we pro­ceed by fixing two points along the true fron tplane. Connect the drawing table with thestereo-plotter and set the floating mark atpoint 1. The same point is set on the controlsheet, which is inserted under the drawingtable. Proceed with the two hand wheels andthe foot disc along the surface line to point 2.If a scale-error is found here, it is best to

~[

~

0DDL "

0D0"

DD0

A

B

4-55

450

445

PHOTOGRAMMETRY IN ARCHITECTURE AND CONSTRUCTION 559

eliminate the latter by adj usting the base.This procedure should be repeated until bothpoints are free from errors. In normal ex­posures the change of the base has an influ­ence on by which corresponds to HL - HR.By changing bx we have to change by propor­tionally.

In order to reconstruct the three-dimensionsituation to a two-dimension plane, it is nec­essary to have a set relationship betweenpoints on the photographs and model-scale.This is the case for the X, Y, Z axis in a nor­mal exposure, provided the front is parallelto the base. It applies in the case of a swivelexposure only for the Yaxis. I n order to com­pensate for the X and Z differences in theswivel exposure which are caused by theangle-shift from normal, we use the followingmethod:-

The actual distance between the twocontrol points is known. By rotating handwheels X and Z we are able automaticallyto check and bring all surface points on thetrue horizontal plane. After this we drawour model in the elevation plane as if itwere a normal exposure by using handwheels X, Y and foot disc Z for distances.This plane is then reconstructed in accordwith the distance between the control andall other surface points on the new trueplane. A height check at control points 1

and 2 will insure us that the heights are cor­rectly set. See Figure 6. (The point G in thisfigure is the photogrammetrical deter­mined pass-point.)

SUMMARY

It has been shown that accurate economicand rapidly constructed models can beformed through using this method.

Our experience has included the construc­tion of 54 models. This provided the oppor­tunity to prove that the method is workablein a great variety of situations. Its accessi­bility to any object makes it far superior tothe classical method.

The results indicate that the photographicmethod is sufficiently accurate for obtainingobjects.

In closing we should point out that whileour remarks apply only to Architecture, themethod can also be used in Archeology, Min­ing Developmen t and other civil engineeringconstructions.

ACKNOWLEDGMENTS

I express gratitude to the Director of thePhotogrammetric Institute of the Swiss Fed­eral Institute of Technology, Prof. Dr. M.Zeller, for giving me the necessary facilities.Only through his help was it possible for meto complete this project in so short a time.

Forestry Applications of Aerial

Color Photography*tRUDOLF W. BECKING,

Dept. of Forestry, Agricultural Experiment Sta.,The Alabama Polytechnic Institute, A uburn, Ala.

A ERIAL photography has played an impor­n tant role in developing forestry sincefirst applied in 1920 and particularly after1940 in the U. S. and Canada. It is highlyvalued by foresters, because it serves as an

excellent record of contemporary forest condi­tions. In fact, aerial photographs comprise oneof the best obtainable forest records, sincethey can be consul ted and supplemented atany time. Foresters have made use of aerial

(Abstract is on next page.)

* Presented at the Society's 25th Annual Meeting, Hotel Shoreham, Washington, D. C. March 8to 11, 1959. This paper is a part of the Panel on The Application of Color Photography in Photo Inter­pretation.

t For making their aerial color photography available for inspection, the author is much indebtedto R. C. Heller, Beltsville Forest Insect Laboratory, Beltsville, Md.; P. R. Wheeler, Southern ForestExperiment Station, New Orleans, La.; Wm. A. Fischer, Photogeology Section, U. S. Geologic Survey,Washington, D. c.; and H. E. Seely, Forest Research Division, Ottawa, Ontario.