a photogrammetrically derived surface?
Fig. 7 shows a portion of an aerial image covering three
apartment buildings (top) and a wire frame diagram of
the laser data of the same area (bottom). We used the
laser data set in the sense of S», that is, as a sequence
of unrelated points. The necessary surface patches of
S1 were obtained from measuring the stereo model on a
softcopy workstation.
Figure 7: Aerial image patch showing an apartment com-
plex of the test site Ocean City (top). The laser data set
of the same area is represented by a wire frame diagram
(bottom).
We skip the details here but present a short summary
of the results. Fig. 8 (left) shows the laser surface rep-
resented as a gray level image. Superimposed are the
photogrammetrically measured points (crosses) and a
few triangles that were formed when generating a TIN
model. The triangles served as surface patches SP. The
parameters found by our approach indicate very good
agreement between the two data sets.
A more meaningful check is to perform the transforma-
tion with the parameters found, followed by computing
the distance of the transformed points to the surface
patches S,. The average distance of 0.03 m between the
laser and stereo surface confirms the accuracy potential
of both methods. Fig. 8 (right) is a graphical illustration
of the matching. The white crosses show all the laser
points that were found as correct matches.
Finally we show the result of detecting blunders. In the
area examined, one laser point did not correspond to
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999
Figure 8: The left part shows the laser surface repre-
sented as a gray level image. Superimposed are the
points measured photogrammetrically. Also shown are a
few triangles formed by generating a TIN model. The re-
sult of the establishing the correspondence between the
two surfaces, the laser points that were matched with
the triangles are shown in the right part of the figure.
any surface patch. As discussed in the previous sec-
tion, such points are labeled as blunders. Fig. 9 depicts
the laser point and the triangle to which it should corre-
spond. A closer analysis reveals that the laser point is on
top of a tree. The planar surface patch, determined by
photogrammetry, is on the ground. Hence, the distance
from the laser point to the surface patch exceeded the
tolerance.
Figure 9: Small squares identify correct matches of laser
points within one triangle, established by photogram-
metry. The cross identifies a point that should lie on the
triangle. However, the distance exceeded the tolerance
and the point is considered a blunder. The laser foot-
print is on the top of a tree while the surface patch was
measured on the ground.
6 Conclusions
Comparing surfaces is a frequently occurring task and
a prerequisite for merging data sets that describe the
same physical surface but with different sets of discrete
points. If the two data sets are in different reference
systems then the comparison is quite challenging be-
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