Analitik fotogrametri ile yöneltme elemanlarının bulunması ve yataya indirgeme (yeni bir yöntem)

Abstract

The object of this presented paper is to deyelope a new analyti cal method that would make it possible to convert the tilted photographs Jar 'to the vertical jthat is to reduce the positions M points on the inclined »si or oblique photographs to the horizontal plane, and also to determine a» the elements of relative and absolute oriantation of any photograph with ân high speed accuracy; The problems of this kind were previously dealt by quite a num - ber of scientists in different ways and for various purposes. Any of those methods and formulas, previously used for the solu tion of the problems, do not permit to determine,as accurately as tbf hew method, the tilt of the photographs and its effects on to the compu ted coordinates' of all other points intended to be reduced to the horizon tal plane. The data required, in additidh to three ground control points in ' the covered area of initial picture, for the determination of the orian tation elements of the first and successive overlapping photographs and also reduction of coordinetes as well as the computation of ground coor- dinetes of the points within the area of overlapping aerial photographs, are restricted only to the picture coordinates of the images of points in question on the tilted photographs that may be measured in any type of comparator or using any plotting instrument. vii The picture coordinates, thus measured and to be used in the com putations, are of course subject to the corrections for the curvature of the earth, refraction of the rays of light, distortion of camera lens and also for the shrinkage of film. The measured coordinates should therefore be first corrected be fore they are used in the new rigid formula. These corrections, as mentioned above, can be determined and applied to the measured coordinates, in other words the coordinates can be corrected, easily by means of any of the transformation formulas, the computer programmes of which are already available and are being used in carrying out of aerial triangulation computations as ihany ohter methods. In addition to these preparatory measurements and computations, for the benefit of the speed and accuracy, the elevations of tie points in theoyerlapped areas are predetermined by terrestrial measurements or by stereoscopic determination in any plotting instrument used for analogue ?» triangulation. It may also be pointed out that in the application of the new rigid formula, for computation of the oriantatipn elements and for the reduc tion of the photographic pointsk to. the horizontal,, the systematic errors do not occur at all. but if its expanded form is used by dropping out hing- feer terms than the first term, the systematic errors become effective as in the case of other methods that generally based on the Gruber' s formula,, The systematic errors thus occur of course can not be detected because of the forced fittings by transformations in power Series of second and higher order >' and since due its behaviour^ scientists have generally considered and adopted it as accidental errors and consequ ently their effects tried to be eliminated or distributed to the points by least square adjustment alone. But even in ai| high degree of fitting, the assumption of undetectable systematic errors msipccidental errors may diminish the accuracy of the computed oriantation elements and reduced coordinates and also introduce new errors unjustly to some points and conceal the systematic errors in those points. viii ^ Iiı the ease of large tilt, this disturbing inaccuracy would natural*- ly be more apparent, whereas the new medhöd, even for obligüe photog;-- raphs, furnishes a very appropriate result free of this systematic error mentioned above. ' Thus, the only error remans is due to the inaccuracy of measure ments which has to be accounted for accidental nature and can therefore be handled by least- square adjustment and consequently a more appro priate result, compared to the other methods »would be obtained in this l^s|)ipettoO,i,:''';'''.î ?;'?'? ?'?;.-.?'' ??--: fî ;:?:/?.;.,?.?;?? ??^ /--'"..,/ / The effect of the small errors of the oriantation elements themsel- VeSiln a single picture as well as in the process of bridging, might be accidental; But the erafor due to the lack of the higher terms than the first ah of the expanded form of the new method or the application of other met - hods, is eönsiderable large and of systematic nature. If an appropriate and more precise results in highly tilted photograph are preferred» it can not be assumed as accidental, though it migKt give that impression; and concealed by double summation or any kind of adjustment or compu tation. andyj (U)) angles. ? ?.,,. R^^vnr,uk^-i ; 4. The computation of eoordinates of exposure station, by using, any well known resection methods with the resection angles determined photogrammetrically,, :»: ??..:?../??/<>? H-».»*//- ?.?..'Sjl'^.-v: ?...??.' ?????. -.?....??. -'- :: i ''.'i^H>.4 w- ? 5. The mathem atical rectification of the tilted photograph by,redtt icing the coordinates of the images of points on the tilted phptographito, the horizontal plane. ;.; ?'??:.-/??. ;r ?.? - ? ?? ?. ?-;???: ???.,. \ ),. \i^,[)-y 3,dT 6" The computation of ground coordinates of\the^Pjoi.^J;.^be,dejb^y- ? mined without terrestrial survey. ? '?.,?????..:>&.. -??:-,/kwvb:4<<;; "' ???? ?'?"?'.... ???;"..';.; v'vi-''V> şî'.'j İO ia%s 7. In addition to the analytical rectification of tilted photographs,,-; described above» it can also be observed that, in developping, the formu lae to be.used in reduction, certain important benefit, as indicated be^ İÖW, are also gaiüedo. :?:!:???'?-.. f i-li i: \';i ;je ;.«?.;.'* hi«K a. The use of rigit formula is very easy and convenient to handle and gives exact results, as far as any accuracy desired for any kind of photogr aphy, regardless the am ount and the degree tq! k tilt of the photograph to be rectified..» ^ / v,! ; ? ^ı. d b. The application of the expanded form of the* formula derived ^h can permit the use of the terms of any degree depending upon j the tilt and accuracy of the result desired or required. c. It is evident and can be proved that the formulae introduced *J and used by Otto V. Gruber and others that generally based oh the same consideration are only a ş'peölal.öM©!^,^,1^^..T^"' t hod taking only the first order term S of the f pr m.u|ş! 4ev^îoppe| by the author of this paper. ' ' " "''""", " "'"'' ""u '**'' *"'" ıv.r-sîi:-' -mU d. The formulae and the results of the solution of any similar prob lems, using the assumption based on the Otto V. Gruber designa tions, were shown to be approximate and can not meet the resp ired accuracy beyond the tilt even not exceeding two three degrees 8. Finally, it is considered benefitial to draw the attention to the followings: a. Appropriate programmes were prepared for electronic compu ters in order to facilitate computations and increase the seeped and accuracy. b. The new method is quite suitable to be applied to aerial trian- gulation, especially to the single picture or single model aerial triangulation. c. The method is most promising to be applied to any other anal- lytic al computations and mechanical rectificationsor plottings, d. Still new and better programmes can be prepared for wider and extensive application of rigifl and expanded form of the formulae of the new method worked out in this paper.