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(c)
Figure 4. (a) first return height minus last return height (b)
gradient based on last return heights (c) filtered
discrepancy map between first and last
2.2 Local statistical analysis and interpretation
The surface smoothness was tested through local statistical
interpretation. The height variation over a small region is an
excellent tool in LIDAR data segmentation (Mass, 1999). Each
height group that lies within a small square area will be fit to a
plane. The iteratively reweighed least squares adjustment
algorithm was used to solve the overdetermined system and
obtain the surface parameters (Mikhail, 1976). Weights were
assigned to each observation based on its residual, except in
the first iteration all observations were weighted equally. After
the last iteration in the adjustment procedure, the root mean
square error (RMSE) was computed for each square window
and recorded at the center of that window.
The number of height points that are included in the surface
fitting procedure depends on the window size. For example, if
we have a window of 3x3, then the number of observations is
equal to nine. Moreover, each of the nine observations is
included in the adjustment nine times in nine different
windows. Each one of those windows has a different RMSE
since it was calculated using different observations. So, the
height point might belong to any of the windows that contain
this point. The attribute used to classify the point is the RMSE.
So, the point will belong to the window that has the minimum
RMSE, in order to obtain the best fit to maximize the surface
smoothness. A high RMSE indicates an irregular surface that
can be interpreted as a characteristic of a tree or a rough
surface, since most buildings have smooth roof surfaces. With
a few number of iterations, all high variability surfaces were
detected and filtered using a minimum filter with a size equal
to the fitting window or larger. The resulting digital surface
model (DSM) of the two filtering steps is shown in figure 6.
(b)
Figure 5. (a) last return heights before first step filtering, (b)
result after first step filtering
Figure 6. the filtered last return image heights
3. BUILDING FOOTPRINT DETECTION AND
DELINEATION
Detecting buildings directly from the raw LIDAR data is not a
straightforward problem. This is due to the ambiguity of other
vertically extended features which are not buildings in the raw
data. Filtering “noise” such as trees and other extraneous
objects facilitates the detection of building footprints and
consequently the reconstruction procedure. Using the ground
plans as in (Brunn and Weidner, 1997) or utilizing a
multispectral reflectance for the segmentation as in (Haala and
Brenner, 2000) are alternatives to the filtering step to obtain