126 GRAPHICAL OR NUMERICAL PHOTOGRAMMETRY?, V D WEELE 
c. the errors in measuring the coordinates of the plotted point with respect to the map 
grid with a standard deviation of m,. 
The comparison between map and terrain will therefore give differences with a 
standard deviation m,, that might be obtained from the formula: 
mn 2 — an 2 | m2 24 2 
m My Fm2 + m2 + m, 
02-42-4024 m2--10m2--m? 
zm qug-mg-tmnm24m?t-m?lm, (2) 
A similar formula can be set up for the case of numerical photogrammetry. 
Here m, will be replaced by m',, assuming that the absolute orientation of the model 
will be found by computation, which may give a precision different from, and probably 
slightly better than, that obtained by the graphical procedure. Moreover m, will be re- 
placed by m’, being the standard error in reading coordinates on a dial, including the 
mechanical errors of the device. 
The comparison between the numerical results and the terrain coordinates will thus 
give differences with a standard error m, to be found from: 
m 2-q23m.2-3923--32--.? 9 
m, my + mg? + m2 + m2 + m, (3 
To simplify the comparison of m,, and m, we will assume that, by a very carefull 
procedure, m, = m, so that 
m2+me2+tm2tm2=m2+ m32+m2+m2=m?2 (4) 
Hence: Mp2 = m2 + m2 + m2 (5) 
and m2 = M2 + m2 (6) 
For many instruments m, will be greater than m,, , but even if they are equal, or can 
be neglected, the comparison between (5) and (6) shows that the graphical method is less 
accurate than the numerical one. 
From the tests, published by Comm. IV at the Congress in 1956 we can derive that, 
for planimetry, m, = appr. 12 micr. expressed on the scale of the negative for signalised 
points (where m,; = appr. 0). 
If we assume that m, = appr. 0.15 mm on the map, we find: 
(m,, cm)? — 144 a? + 225 b2 + m2 (7) 
(m, em)? = 144 a? + m2 
where a = Photoscale expressed as f . 10—4 
M 
b — Map scale expressed as 10 (M = 500, 1000 or similar value). 
As far as elevations are concerned a difference between graphical and numerical 
restitution does not exist in the measurement and use of spot heights. A difference may 
occur due to the application of a numerical absolute orientation by a linear transforma- 
tion as against an empirical absolute orientation including the introduction of model 
deformations based on the height errors obtained. 
A more important source of differences results if heights are represented by contour- 
lines. The precision of elevations found from interpolation between contour-lines will gen- 
erally be less than that of a spot height. On the other hand, the representation of the 
terrain by digital data, will hardly be so clear and complete as by contour-lines and can 
only be considered as practical for pre-chosen profiles. 
The precision of elevations will therefore have only a minor influence on the choice 
between graphical and numerical photogrammetry.