n be 
the 
rete 
(18) 
rete 
FT. 
1 be 
and 
19) 
the 
the 
hen 
acy 
S, 
ts 
se 
he 
it 
nd 
of 
of 
ed 
ne 
on 
n 
the grid points (sampled and interpolated) on 
the modelled surface of the patch. 
Goo 7 TZ v? NE (20) 
PS 
Where V?. represent the discrepancy between true 
and modelled heights, and N, is the number of 
points in the patch. 
For comparison with other tests, the mean error 
is normalised vith the maximum height in the 
Ope = Opo/H (21) 
The mean error o S (of CS) for comparison vith 
Opc» W8S estimated for the same number of points 
(N°) as used for o,.. Outside that area, there 
are no discrepancies. Thus 
2 
Ocs = i« V5/N,) (22) 
where V, is the discrepancy between the modelled 
and the true height. The number of sampled 
points and the number of interpolated points are 
obviously not the same as in the case of PS, 
however the total number of the points is the 
same. 
This mean error can also be normalised by Hoax 
ers = cs Pnax (23) 
In each experiment the maximum discrepancy 
between the ideal and the interpolated DTM 
surface was normalised by Ho x? i.e., to have a 
measure that is independent Of the height of the 
primitive: 
MAXER = maximum discrepancy/H ax (24) 
The sampling efficiency is defined by the number 
of sampled points per unit area: 
T = [Numb of sampl. pts]/ 
[total Numb. of pts per grid] (25) 
For comparative assessment, the relative 
differences in performance and the ratios of the 
performances are suitable. This is because a 
relative difference is a measure of gain or 
loss, while a ratio is independent of the 
magnitude of the errors. 
Ac = gain (+) or loss (-) in 
the mean error o, (26) 
Ratio of the mean error of PS and CS: 
Ro = Opnl/O (27) 
css. 15. C8 
Ratio of the mean error for CS3 and CS2: 
R = 0 /G (28) 
Ses (33/0082 = SC). BO) 
A MAXER : = increase or decrease of 
the maximum error, (29) 
Ratio of the maximum error of PS and CS: 
A - MAXER,,/MAXER (30) 
HAXER 5 /ps PS CS 
Ratio of maximum error of CS3 and CS2: 
R = MAXER /MAXER (31) 
MAXE 3 
Fcs(3)/CS(2) CS (2) Core) 
À E = gain or loss in the efficiency (32) 
Ratio of the efficiency of PS and CS: 
R - RR (33) 
Ratio of the efficiency of CS3 and CS2: 
R 
E (34) 
CS(3)/CS(2) 
= Res(2)/Rcs(3) 
4. OPTIMUM SAMPLING APPLIED TO REAL TERRAIN RELIEF 
To verify and consolidate the conclusions drawn 
from the experiments using artificial ideal 
geometric primitives and their composite some 
experiments using real terrain relief as the input 
vere conducted. A realistic S-factor is S=1/16. 
4.1 Experimental test 
4.1.1 Haifa region Aerial photos were 23 x 23 
cm, Scale = 1:30,000, c = 150 mm Camera type = 
Wild RC 10, the Easting of the area was between 
145.000 and 147.000, the Northing between 220.000 
and 225.000 The area selected for testing was 
composed of partly rough and partly smooth 
terrain, the altitude of terrain was between 
H - 164.992 m and H . = 9.708 m. The flat part 
max min 
of the area was used for agricultural purpose, and 
the rest was covered partly by small trees and 
bushes, and partly by a few buildings. The instru- 
ment was KERN DSR-1 Analytical stereoplotter. 
a. Selective sampling: 
Two regions with some abrupt changes have been 
delimited from a more homogeneous terrain, with 
the break lines acting at the same ‘time as the 
peripheral lines. These lines were sampled 
selectively, by using the MAPS 200 system I-set 1 
(figure 8). 
Inside these regions the break lines and break 
points which fulfil the specifications of the rule 
base were sampled selectively, by using MAPS 200 
system, I-set 3 (figure 9). 
All the break lines which fulfil the 
specifications of the rule base, except the break 
lines joining the peaks, were sampled selectively, 
by using MAPS 200 system, I-set 2 (figure 10). 
  
1 | 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Figure 8: 
I-set 1 
Figure 9: 
I-set 2 
Figure 10: 
I-set 3 
83