ding extraction
he topographic
osed procedure
smatic building
le of Minimum
ur approach.
ur Information
durch die von
fahrens nutzen
rasentiert wird.
alls basieren auf
he Datenquelle
SM consists of
ction of build-
bout the build-
netric and pris-
owledge about
e building rele-
t space related
and resolution
stner, 1995] we
r approach, in-
struction. The
f the automatic
n of buildings.
imum Descrip-
ion of prismatic
hortly describes
of the general
sults for the IS-
describes, how
1 our approach,
PRINCIPLE
n 4 is based on
h (MDL). This
ate the param-
ramework, and
ildings by inte-
scription length
del and the de-
plexity depends
the number of
observations. The deviation of the data from the model is
given by the weighed squared sum of the residuals €) of a
ML-estimation.
Let the following model be given
E(y) = g(8), D(y) = Euy (1)
where G denotes the u x 1 vector of unknown parameters,
y the n x 1 vector of observations and X, their covariance
matrix. The description length [Rissanen, 1987] follows by
Q
2 in2
DI + = Ibn (2)
where €) is given by
Q = [y — &(8)] X, y — e(8)] (3)
Following the principle of MDL, we search for the description
which minimizes (2), thus selecting the model and fitting the
data to the model simultaneously.
In order to decide whether a difference in description length
between two alternatives is significant, a hypothesis test
based on the variance of DL can be applied. The variance
of DL follows by error propagation taking the variance of N
into account, which is 2 (n — u), and thus
dor ien (4)
3 BUILDING DETECTION
The first step towards building extraction is the detection of
possible building areas in order to focus the later steps of
reconstruction on these. The principal idea of our approach
to building detection is to isolate the information about the
buildings within the DSM and to segment this data by bi-
narization using a building related threshold, e.g. the height
of a floor. Therefore, we first compute an approximation of
the topographic surface. There are different ways which can
be followed for this purpose. In our approach, we use math-
ematical morphology (here: opening). As an alternative of
such an opening, a dual rank filter, which is a modification
of the opening, can be used. The modification is to use the
median of the minimal and maximal p% values of the applied
structuring element [Eckstein and Munkelt, 1995] instead of
the minimum and maximum itself. This approach has some
advantages compared to the opening, because it compensates
for noise and outliers in the data. For the data sets we use
here the difference between these two approaches show only
minor effects on the following steps, because the percentage
of outliers seems to be small.
The difference between original DSM and the approximation
of the topographic surface contains the information about the
buildings, approximately put on a plane. Due to this fact, a
binarization with a given threshold yields a first segmentation.
This segmentation shows some deficiencies due to some ef-
fects of the DSM generation, e.g. round off at building edges
due to regularization, and global thresholding. Furthermore,
the first segmentation may include segments, which are higher
than the surrounding topographic surface, but which do not
represent buildings, e.g. trees. In order to overcome these
short-comings, we first select only those segments, whose area
is greater than the expected minimum area of buildings, and
then refine the segmentation by adapting the threshold lo-
cally based on the height information within a bounding box
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Data
Determination of an approximation
of the topographic surface
Computation of difference
Difference
Initial segmentation
Selection of segments
Refined Segmentation
î Segmentation
Figure 1: Building Detection
(3
101
115 a
A PA 113
= «116
s
Vu < m
Cun UN e
^, A4 \ y
Se
NN DI ^
N
SR, A
A137 134 ZN
a N e m
Figure 2: FLAT: gound plan labels
En
