ge displace-
on. Now we
, Say, half of
)- $ we con-
ig conjugate
idow size to
' enough.
itching win-
licting their
aints
ig the orien-
of partially
equent pho-
matic gener-
sks must be
ic aerial tri-
ls new prob-
iltiple over-
requires the
ealistic over-
at selecting
3 more accu-
ailable from
otprints, the
t be known.
rmine in the
know in the
ct of match-
ns and the
ed an inter-
1+2. In or-
roximate lo-
he matching
| the conver-
ull-in range)
)CESS.
or. It works
ith selecting
| by project-
> back to the
Figure 3: Example of 6 overlapping images.
image i
projected position
in object space
Figure 4: Schematic diagram of predicting conjugate
locations.
images that are involved in the matching procedure.
The result of the first step is an uncertainty figure in
the object space, symbolized in Fig. 4 by an ellipsoid.
This figure is a function of uncertain exterior orienta-
tion parameters of image i and uncertain elevations—
usually the dominating factor. Thus, the figure has
an elongated shape in the z-direction. The projection
back to the other images results in the predicted po-
sition and in the uncertainty figure that determines
a plausible search space. The figure is further influ-
enced by the uncertainty of the exterior orientation
of image k. The second mode of the predictor be-
gins by selecting an entity in object space followed by
predicting it to all images involved. In that case the
uncertainty figure in object space is pretty much re-
stricted to a vertical line with the centroid being the
estimated elevation and the length being the uncer-
tainty of the estimate.
Because the influence of uncertain elevations on the
matching location and size of the search space is often
741
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Table 3: Uncertainty factors for predicting conjugate
locations due to inaccurate exterior orientation and
elevations.
errors in EO errors in
position attitude elevation
AP Ah
I | £p [deg] | £a = | En
0.001 | 0.001 || 0.01 | 0.0002 || 0.01 | 0.010
0.01 | 0.01 0.1 0.002 0.3 40.711
0.05 | 0.05 1.0 0.022 0.2 (0.25
0.1 0.1 9.0 0.122 0.33 | 0.5
underestimated, we elaborate further on this subject.
Table 3 contains three different coefficients € which
show the influence of an error in position (ep), at-
titude (£a), and elevation (ea). The errors on the
predicted conjugate locations are obtained by mul-
tiplying the coefficients by the base. For example,
ep = b- Ep gives the error in the predicted location
as a function of the uncertainty in the position of the
projection centers. Likewise, ea = b - €, indicates the
error as a function of uncertain attitude data. Finally,
en = b-Ep is the error because of uncertain elevations.
The first column expresses the uncertainty in posi-
tion of the exterior orientation, AP, as a ratio to the
flying height H. Consider a large-scale aerial triangu-
lation project for a moment, scale 1:2000, and a wide
angle camera. Then the first entry means that the
position of the projection centers is fairly well known
(0.8 m). The first entry of column 3 indicates that
the attitude is also well known. The first row reflects
the situation where accurate GPS/INS data are avail-
able. The fourth row is more representative of flights
without additional information. An error of 5? in at-
titude leads to an error in the predicted position of
ea — 88-0.122 — 10.8 mm, assuming the base is b — 88
mm.
A closer examination of the coefficients reveals that
the uncertainty in elevations has a much higher in-
fluence on the predicted position than errors in the
exterior orientation. For example, the first entry in
column 5 refers to a situation where all elevations are
either well known, or where a very flat surface is as-
sumed. The ratio of elevation uncertainty, Ah, to
flying height, H, is most likely considerably larger.
Mountainous areas may have elevation differences as
much as 1/3 of the flying height. In this extreme case,
the uncertainty of the predicted conjugate location
would reach half of the base. Table 3 also demon-
strates that even if the exterior orientation is well
known the predicted locations suffer from unknown
topography, a fact that is often overlooked.
5.2.3 Multiple Image Matching: The problem of
matching more than two images is approached in dif-
ferent ways. À more pragmatic solution is to employ
