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Commission IV Invited paper 125 
Graphical or Numerical Photogrammetry? 
by A. J. VAN DER WEELE 
Delft. 
I. Introduction. 
This paper will not deal with the purely technical aspects of the question: graphical- 
versus numerical photogrammetry, which belong to the field covered by Comm. II, but an 
attempt will be made to treat the subject from the point of view of method. 
The choice between graphical and numerical photogrammetry will depend, in a very 
general way, on considerations including required accuracy, economy and the organisa- 
tion of the procedure. 
Furthermore the field of activity on which photogrammetry is to be applied is very 
important. In this respect we will treat separately the application for cadastral and for 
technical purposes, because, in these two cases, the problem has completely different 
aspects. 
The author does not have the pretention that he will be able to give a definite and 
conclusive answer to the question posed by the title of his paper. No final conclusion is, 
therefore, thought to be possible, and any tentative conclusion reached must be subject 
to constant review on the light of current and future developments. He therefore will 
limit himself to an attempt to give a review of the various factors which should be taken 
into account in making a choice between graphical and numerical procedures, leaving it 
to the reader to give his own weights to these various considerations. 
H. 
The graphical and numerical methods of application of photogrammetry have both 
the same starting point. This is the model which is obtained in a restitution instrument 
after a relative and absolute orientation of a pair of photographs. 
A graphical method is applied if the position of any point, which is covered by the 
measuring mark, observed in the stereoscopical model, is fixéd by plotting it on a map 
sheet. 
A numerical method consists of reading the coordinates of the point on appropriate 
dials, using these data as a basis for further computations. 
A first comparison may be on terms of the precision of the result. 
It will be assumed that the metrical precision of a point in the model ean be charac- 
terised by the standard error m, This standard error expresses therefore the precision 
of the intersection of two corresponding rays as a function of the precision of the orien- 
tation-elements of the two cameras. m, depends on the precision of the observation of 
parallaxes and of the coordinates of the points used for the absolute orientation. 
The standard error in setting the measuring-mark on a point, will be denoted by "og. 
If the eventual mechanical errors in the transmission of the movement of the meas- 
uring-mark to the pencil or needle on the plotting table can be expressed in a standard 
error m,, the standard-error in the position of the plotted point m, will be found from: 
9 9 9 E 9 
My? = Mg? + me + my, (1) 
If the map position of the point is compared with the position of the corresponding 
point in the terrain, the difference which may be obtained contains three additional 
sources of errors viz: 
a. the error in the interpretation of the chosen detail, with a standard deviation m;; 
b. the errors in the terrestrial coordinates with a standard deviation m,;