nodel coordinates' 
lative orientation 
transformation on 
ce propagation is 
sformation. 
igation expressing 
ors is defined as: 
iub Wy 
1e absolute 
1e model 
s component con- 
e to the computed 
el coordinates de- 
at the scale of 
+1.5m to the co- 
re, as the control 
he model coordi- 
ctive. 
pters describe two 
ation implementa- 
ived from photo- 
; usually evaluated 
SD and is consid- 
hole stereo-model. 
es through out the 
1at measurements’ 
el are smaller than 
edges. The error 
formulated above, 
tion of the meas- 
s evaluation of er- 
S, illustrate the SD 
resenting them as 
p enables a more 
accurate SD evaluation in comparison to the 
use of a fixed value. Figure 2 that is taken out 
of a stereo-model at the scale of 1:40,000 
based on ground control points (that are basi- 
cally pass points) with a precision of +5 m, il- 
lustrates a typical form of that kind of a map 
(errors depicted in centimeters). 
  
  
  
  
  
Fig. 2. Small scale model - equi error contours 
The map demonstrates two aspects, the 
first refers to the SD behavior and the manner 
by which it varies through out the model, and 
the second aspect refers to the rate of change 
from the center up to the model edges. The 
contours in that figure (represent a typical ste- 
reo-model for mapping) varies between SD of 
+3 m at the center up to SD of +4.4 m at the 
edges, a range of 1.4 m which cannot be ne- 
glected. 
The equi-error contours are generated by 
the use of a widely spread and dense enough 
set of measurements, that by computing it’s SD 
(for each measurement), and applying a rele- 
vant contour generation algorithm (where the 
accuracy replaces the height), equi-error con- 
tours are defined. As for the data set, the DTM 
grid (although it is not necessary) is the best fit 
data set for this purpose. 
3.3 Profiles 
À profile SD evaluation demonstrates 
another purpose of the error propagation 
mechanism, the one refers to the applications’ 
results evaluation. The profile, which is an es- 
sential tool for planing and for terrain's analy- 
sis, is defined as a set of measurements along a 
line, that are usually collected by direct meas- 
13 
urement or computed by DTM interpolation, in 
order to observe the surface shape. The profile 
type, discussed in this chapter, is the one gen- 
erated by direct measurement. 
Profile's accuracy is evaluated by the de- 
termination of the altimetric component's vari- 
ances. For each data point The variance is ex- 
tracted from the point's computed variance- 
covariance matrix. It's graphical representation 
is illustrated in Figure 3 (the profile is the thick 
line and the SD lines are the thin lines). 
A 
100 7 
50 — 
  
  
v 
0 T [ I 
0 500 1000 1500 
Fig. 3. A profile’s SD 
The SD determination is essential, espe- 
cially, for the evaluation of derived applica- 
tions, such as: evaluation of volume's SD, or, 
for visibility determination. 
4. COMPUTATIONAL APPLICATIONS 
While chapter 3 demonstrated the im- 
plementation of the error propagation mecha- 
nism for applications that are based on the 
evaluation of single measurements, practically, 
most applications involve several points that 
are related by computation. Therefore inter re- 
lations are to be taken into account and the SD 
evaluation refers to the computations’ results 
and not to the measurements. 
4.1 The covariance between measurements 
Since data collected from photogram- 
metric stereo-models are transformed by the 
same transformation equations and parameters,