KXIX-B3, 2012
atrix. For each build-
calculating the mean
pixels. After smooth-
sharp building walls,
to D»(z, y) matrix.
idering the roof-type,
only a single height
1 is equal to building
a gable-roof, we fol-
building complexity.
ex building as struc-
1), then we can find
e-dimensional space.
| segment using Har-
Stephens, 1988) over
sides, we also detect
ck each building cor-
| ridge-line endpoint.
osest ridge-line end-
. À detailed demon-
irmacek et al., 2011).
ned to corresponding
is detected as a com-
ould not be extracted
ame idea for building
ooftop reconstruction
? building rooftop re-
ding rooftops and for
dge-line properly, we
Dy (x,y) matrix.
natic Models of Build-
odel of buildings ac-
on CityGML standard
th approximation and
Two algorithms are
g polygons based on
fi et al., 2007). The
nber of main orienta-
ollows:
ar polygon, i.e., sides
he top view, a method
ole (MBR) is applied
op-down, and model-
imizes the initial rec-
etails of the data set.
oximation is presented
main orientation, the
orientation, as shown
R image (Fig. 5(b)) is
egion. After subtrac-
ig. 5(c)). For any of
| (Fig. 5(d)). They are
ing regions produced
strated in Figure 5(€)
process is followed
subtracts them from
archical procedure is
uced any more. That
no new regions CIE-
] regions is less than
:e the final polygon i$
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012
(a) Rotated building
(c) Rotated region - MBR region
(e) New regions produced by
subtraction of (c) and (d)
(b) MBR image
(d) MBR on small regions
(f) Superimposed final rectilinear
polygons (red) on DEM
Figure 5: MBR based polygon approximation
rotated back to original orientation (Fig. 5(f)). In this figure
the red lines highlight the rectangular polygons.
e If the building is not rectilinear, i.e., at least one side is not
perpendicular to the other sides, a method based on RAn-
dom Sample Consensus — RANSAC (Fischler and Bolles,
1981) is applied for approximation.
RANSAC was originally devised to robustly fit one single
model to noisy data. It turns out, however, that it can also
successfully be used to fit a beforehand unknown number of
models to the data: In the case of the ground plan bound-
aries the number of line segments is initially unknown. We
simply apply the method repeatedly — always deleting the
already fitted given points from the input data — until either:
3) we consider the lines found so far sufficient to construct
the ground plan completely or
b) the number of points fitting to the best line segment with
respect to the current iteration step falls below a chosen
threshold f.
In this algorithm the straight lines are repeatedly extracted
using RANSAC algorithm and merged to form the final poly-
gon. Figure 6 shows the RANSAC based approximation of
the same building represented in Figure 5.
As an alternative to the RANSAC based approximation algo-
rithm, à method similar to MBR-based is proposed for the build-
Ings containing several orientation directions. The method called
Combined Minimum Bounding Rectangle (CMBR) based algo-
rithm for hierarchical approximation of non-rectangular polygons.
In this method, based on each orientation a MBR (rectangle)
polygon is estimated as first approximation level, as shown in
Figure 7(a and b).
Intersection of the rectangles corresponding to each orientation
produces the first approximation of non-rectangular building (Fig.
327
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
Figure 6: Approximation of polygon obtained using RANSAC
(a) MBR model 1 (red) (b) MBR model 2 (red)
(c) Intersection of two MBRs (d) Remaining regions in first orientation
(e) Fitting MBR to remaining regions ^ (f) Approximation based on two orientation
Figure 7: CMBR based polygon approximation
7(e), yellow region). The first approximation area is subtracted
from original binary region to generate the remaining regions
which should be approximated. The process is continued, simi-
lar to the MBR-based method but using all orientation directions,
until no more regions remain or remaining regins contain small
number of pixels. Figure 7(f) illustrates the final approximation
result of the sample building by using two main orientations. The
approximation result could be improved by taking into account
more significant orientations.
The proposed algorithms for approximation of the building out-
lines and finally, generating 3D prismatic models have been im-
plemented in a city area containing flat roof buildings in Tunis
(Fig. 1). For this experiment, two approaches of MBR- and
