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,