International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
On building edges, two points within a few centimeters could
have a great height jump since one might be on the ground and
the other one is on the roof. Such outliers were detected based
on the statistical interpretation of the computed discrepancy and
mainly on the computed standard deviation of the
discrepancies. Consequently they were deleted from the data
set to eliminate their influences. The test started with points
within 0.05m or less. Then in order to include more points in
the computation and strengthen the results, the planimetric
distance constraint was increased to include points within
0.10m and 0.25m. However, changing the planimetric distance
and including more points did not change the discrepancy
average in all overlapped regions. Figure 3 summarizes the
behavior of the computed mean relative height offset between
adjacent strips.
As expected, the histograms (for example see figure 4) show
that the relative height discrepancy between adjacent strips has
a random normal distribution. However, the mean of
discrepancies is not stationary and does not equal zero. In the
first. four overlapped regions the discrepancy was within
+0.04m. Then the average discrepancy between strips (5-6, 6-
7, 7-8, 8-10, 10-11, and 11-12) seems to increase up to 0.10m
with a negative sign since the discrepancy was computed by
subtracting the height of the right strip from the height of the
left strip. Then in the last two overlapped regions (12-13 and
13-14) the discrepancy dropped to —0.06m. Therefore the
discrepancy shows a systematic behavior. It shows a trend with
time (North-South direction) since the strips where ordered on
the time they were scanned (strip ! was the first one to scan and
strip 14 was the last). This trend was observed in all the 13
overlap regions that were tested. Figure 5 shows the relative
height discrepancy along the North-South direction in the
overlapped region between the 1% and the 2™ strip. It also
shows the short period variation overlaid on the trend which is
the long period variation. In general those offsets are not purely
as a result of height differences at exactly correspondening
points in the two strips since they are not error free in
planimetric positioning. Consequently, due to this planimetric
uncertainty the compared points might not have the same exact
planimetric position and this miss correspondence may
contribute to the height offsets. This correlation between height
and planimtric offsets is more significant in sloping surfaces.
i Calculated discrepancy in the overlapped regions i
+ _ Uncertainty of the computed discrepancy {
Height diecrepancy m
o
ree
|
|
| i A
o 2 4 6 8 10 12 14
Overlapped region
Figure 3: Mean Relative discrepancy behavior between
adjacent strips, where the x-axis represents the
overlap region (where ] is the overlap region
between strip | and 2)
450 [——— : : : p re
400
350 - | J
Counts per bin
150}
|
sol |
| |
A ul
-0.6 =
| li. eid
0.2 0.4
Quantized height difference (m)
Figure 4: Histogram of the relative height discrepancy between
the 1* strip and the 2" strip.
a
=
2
06
7
calculated discrepancy |
06k | —— Fitted spline H
|. Zero discrepancy line |
04
2
e N
Vertical disrepancy (m)
N
i
2
>
-0.6}
500 5 1000 1500 pe ODD
Northing + 574000 (m)
Figure 5: Relative height discrepancy in North-South direction
(overlap region between the 1* and the 2" strip).
5. DATA ABSOLUTE ACCURACY
Firms that work in collecting data usually publish a fixed
number for the uncertainty of their data. However, these
numbers are usually not verified by the users. This is due to the
fact that this is not a simple task. Correspondence between laser
data points and ground points is not a straightforward matter.
The absolute offsets can be found by measuring the location on
the ground of a point or feature of a known coordinates in the
data set and compare the two measurements. So in order to
evaluate the data set used in this research, a ground survey was
conducted on an area with particular specifications. A large
tennis field, which contains 10 tennis courts, and a flat football
field adjacent to it represent the selected test area, as shown in
figure 6. The selected area has two main useful characteristics.
First, area is flat and horizontal with almost no significant slope
over the tennis courts. This enables the examining of pure
height accuracy since the flatness of the surface rules out any
planimetric uncertainty effects. Second, the presence of
drainage ditches around the field facilitates the computation of
the planimetric accuracy. The selected area covers a full swath.
An intensive control network over the test area was established
using static Differential Global Positioning System (DGPS).
This network was designed to serve the typical topographic
survey over the test area. After establishing the necessary
control around the selected test area, an intensive topographical
survey was conducted. More than 400 points were collected
over that area. Collected points were concentrated mostly at the
critical features such as ditches surrounding the tennis courts.
Figure 6 shows the collected ground points over the test area.
Those points were then used to establish the correspondence
with the laser data based on the spatial positions and
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