XIV. Congress of the International Society for Photogrammetry Hamburg 1980

Transcription

1 XIV. Cogress of the Iteratioal Society for Photogrammetry Hamburg 980 Commissio V Preseted Paper ALTAN, M. O. Techical Uiversity of Istabul Chair of Photograrretry ad Adjustmet A COMPARISON BETWEEN -PARAMETER SOLUTION AND THE BUNDLE METHOD AT A PHOTOGRAMMETRIC CONTROL SURVEY ABSTRACT The recet eergy cr~s~s forces every coutry to built big power plats with large coolig towers. Oe of these large coolig towers workig o the atural draft priciple was erected i North Germay. For documetatio purposes also to check some specific parameters of the geometry of the etire structure high oblique terrestrial photograrretry was employed. The coordiates of the poits o the photographs take from arbitrarily choose camera statios were measured o a ste:reocomparator. The orietatio ad trasformatio ito a locally defied coordiate system were performed with the rigid budle method ad also with the -parameter solutio. I order to compare these two methods the differeces of the three dimesioal coordiates of all object poits are determied. As a result it is show that terrestrial photogramretry ad these two methods give efficiet solutios for such precise surveys. 009.

2 INTRODUCTION I desly populated idustrial coutries big power plats are owadays more ofte built away from atural water recources. Large coolig towers with great dimesios are a commo sight with the uclear power plats, if there ~s o water for coolig purposes. A large coolig tower workig o the atural draft priciple was erected i Nordrhei-Westfale (Federal Republic of Germay). This coolig tower is uique cocerig the evelopig shell. It ~s a prestressed steel cable et structure covered with alumiium sheetig. The et is formed by triagular meshes caused by two diagoal ad oe meridioal set of cables. The whole costructio has a rotatioal form which is defied by 26 meridioal cables. Each of these cables represet a secod order parabolg. The dimesio of the steel r~g ~s 4 mat the bottom ad 9 mat the top i diameter. The upper rig hags from a sleder cetral mast, 80m i height (Fig. l). The parameters of the geometric shape of the whole costructio ad bhus of all meridioal curves were defied through the static calculatios ~ the desig stage. After the structure was fially erected its actual shape had to be determied before moutig the sheetig. The purpose of this cotrol was to check whether the erected from was equal to the desig. Figure. 00.

3 PHOTO GRAMHETRIC SURVEY For documetig ad also to check some specific parame ters of the geometry of the etire structure high oblique terrestrial photogrammetry was employed. To determie the spatial coordiates of the targets which would serv e as cotrol poits for photograrre tric restitutio, a precise traverse was measure d aroud the base of the tower. The three dimesioal coordiates of the travers poits ad of the targe ts were computed by a rigorous adjustmet. As the chaise of the camera statios glve the difficulty of overlappig the ear ad far sectios of the et i the photographs, it was decided to choose the camera statios iside the structure. The JEOPTIK UMK 0/83 camera was positioed o arbitrarily choose camera statios, each positio choose wholly idepedet from ay othe r with the oly goal of photographig as large a sectio as possible (Fig. 2). photograrretric survey, see [4[. For further details of the BOPP, KRAUSS ad PREUSS restituted these photographs i order to calculate the deviatios of the meridioal curves from the desiged shape. They calculated the spatial coordiates of the poits o the mesh with a geeral budle solutio. DATA REDUCTION KARARA ad his group have itroduced the method of the Direct Lieer Trasformatio a few years ago [[ This method establishes a liear relatioship betwee coordiates of image poits, measured with a comparator ad the correspodig object space coordiates. This liear approach for the calibratio of a camera does ot require fiducial marks o the photographs. Usig the advatages of the Direct Liear Trasforma tio, BOPP ad KRAUSS derived the eleve parameter solutio \v ll_!_ch ca also be applied to those cases where the iterior orietatio is kow a d where it should be eforced [3[. 0:.

4 Figure 2. 0:.2-

5 ALTAN, BOPP ad KRAUSS have studied the eleve parameter solutio i coectio with a " semi-metric" camera Hasselblad MK70 j 2 j. I cotrast to this paper the differeces betwee the rigid budle ad the eleve parameter solutio are studied i coectio with a "metric" camera. The budle solutio used i this study is based o the covetioal o- liear colliearity equatios. I this solutio, i additio to the lmage coordiates, the priciple distace of each photo ad the object space coordiates of all cotrol poits are cosidered as observatios. Thus the orietatio parameters of the budles ad the object space coordiates of all poits are determied simultaeously by a least- squares adjustmet with coditio equatios with ukow parameters ad with respect to all possible correlatios betwee the observatios. I this paper oly a diagoal weight matrix of the observatios are cosidered. For the presetatio of the results the differeces of the coordiates of the poits are determied by the mea values MDX = -IjDXj MDY =-IjDYj MDZ =-I jdzj MDP = - 2:: I DX 2 - DY 2 - DZ 2 with DX, DY, DZ differeces of the coordiates, umber of poits i the compariso. The mea values, calculated from the differeces of the cotrol poit coordiates determied by the budle solutio with differet uit weights of the image coordiates ad by the adjustmet of the geodetic measuremets are illustrated i Fig. 3. I the eleve parameter solutio the orietatio or calibratio parameters of each budle are determied i a first o-liear least-squares 0:3.

6 MDX [mm] --- MDX M DY M DZ --MDY M DZ Oo [f.l m] Figure 3 adjustmet where the object space coordiates of the cotrol poits are regarded as costat. The object space coordiates of all poits are computed ~ a secod o liear least-squares adjustmet where the predetermied trasformatio parameters are costats. The cocept of the eleve parameter program allows the computatio of a pure orietatio program if the data of the iterior orietatio are read as additioal iput. COMPARISON OF THE RESULTS OUT OF THE BUNDLE AND THE - PARAMETER SOLUTION For the compar~so of the two methods the differeces of the three dimesioal coordiates of the object poits resultig o oe had from the rigid budle solutio ad o the other had from the two step orietatio respectively o-the-job calibratio are determied. For the presetatio of the results the mea values listed i the followig table are calculated. The compariso of the results of the orietatio ad o-the- job calibratio shows that the results of the calibratio are better tha the orietatio. The orietatio program is calculated with the camera costat give ~ the calibratio report of the camera. The differece of this value from the determied camera costat by the o-the-job calibratio is 43 ~m. This ca be iterprated that eve with

7 the combiatio of a me tric camera the adjustmet with more paramete rs ca g~ve better results. Whether we use the orietatio or o- the-job calibratio solutio the obtaied maximum mea value is ot more tha 3 em. For the case of o- the- job calibratio this value decreases approximately to l em, a mout which is aquivalet to 0. 08%o of the mea object distace. This seems to be acceptable for most applicatios i cotrol surveys. ~X ~y ~z ~p O-the-job 5, 4,7, 0 26, 7 Calibratio Orietatio 2, 5 4, 6 7, 6,2 Table The mea values [mm] calculated from the ll parameter solutiobudle solutio REFERENCES Ill Abdelaziz, Y. I., Karara, H. M.: Direkt Liear Trasformatio from Comparator Coordiates ito Object Space Coordiates i Close- Rage Photogrammetry, Proceedigs of the ASP/UI Symposium o Close-Rage Photograrmetry, Urbaa Illiois, Alta, M. O., Bopp, H., Krauss, H. : Some Accuracy Aspects of O- The-Job Calibratios Show at the Example of a Photogrammetric Cotrol Survey, Proc. of the Iter- Cogress Symp., Com. V, Stockholm, 978. IJI Bopp, H., Krauss, H. : A Simple ad Rapidly Covergig Orietatio ad Calibratio Method for No- Topographic Appli catios, ASP-Fall Techical Meetig, Little Rock, Arkasas, Bopp, H., Krauss,H.,Preuss, D.,: Photograrmetric Cotrol Survey of a Lar ge Coolig Tower, ASP-Fall Techical Meetig,Little Rock, Arkasas, 977. This paper is a part of the research of the author at the Istitut fur Aweduge der GeodMsie im Bauwese Uiversity of Stuttgart sposored by the Alexader vo Humboldt- Foudatio. 05.