d
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itation
urs
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n after
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egularities
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ructed
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tic Models
metric model to be applied, but does not allow a decision,
which group of model should be applied in a common frame-
work. Therefore, we choose MDL as a tool, which is able to
compare different descriptions with different structual com-
plexities. This approach is described in Section 4.3.
4.2 Prismatic Building Models
For prismatic models our approach to shape reconstruc-
tion of the outlines consists of a local and a global analy-
sis step, which can be combined in different ways. Com-
plexity considerations [Brunn et al., 1995] indicate to pre-
process the closed contours in order to elimate discretiza-
tion noise due to the DSM raster using a merging or split-
ting technique and to iterate the local MDL-application —
c.f. [Weidner and Forstner, 1995] for detailed description —
until no changes occur any longer, and then proceed with
global processing, which starts with the derivation of hy-
potheses about the regularities. Due to the transitivity of
parallelism and collinearity, and similar relations including or-
thogonality, these hypotheses are linear dependent. On the
other hand, sets of individually consistent hypotheses need
not be jointly consistent. Therefore, we continue with the de-
termination of a set of linear independent hypotheses, which
is then introduced into a robust global estimation procedure
[Fuchs and Fórstner, 1995]. The height information is com-
puted as for the flat parametric building model Figure 3 shows
an overview of the MDL-based reconstruction of prismatic
models.
4.3 Model Selection
The selection of the model which should be applied for the
description of the building is based on MDL. For this purpose,
all alternative models are computed. Due to the fact that the
ground plan between the parametric models and the prismatic
model differ, different areas of the data are described using
the different groups of models. Therefore, the selection of
the model is not directly related to the description length,
but to the gain in description length compared to the case, if
no model is used.
DSM (section) Parametric models
Selected models
Prismatic models
Figure 4: Selection of models
The number u of free parameters needed to describe the mod-
els are seven for the flat building and eight for the building
with symmetric, sloped roof. Prismatic models are described
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Label 126 128 130
no parametric model | 21105.8 | 10193.1 | 26471.5
# points 1192 625 1459
FLAT 18545.3 3282.7 | 41420.1
SYMSL 1864.2 1080.7 | 234192
gain 13241.6 9112.4 3052.3
no prismatic model 19364.4 9420.4 | 21742.5
# points 1104 583 1224
PRISM 11672.8 2121.3. ] 12016.5
gain 7691.6 7299.1 9726.0
difference in gain 5550.0 18133 | 6673.7
selected model SYMSL | SYMSL PRISM
Table 1: Characteristics of models
by number of polygon points x 2 parameters, if no restric-
tions are introduced, and two parameters for the height in-
formation. The number of observations n is related to the
number of points in the ground plan of the models. (2 mea-
sures the deviations d of the models from the DSM data,
i.e. Q — d? X, d, where X, — 071 was used here with
Oh = 0.4 m.
Figure 4 shows the original data, the results of building re-
construction using parametric and prismatic models, and the
selected models. The characteristcis for some of the models
are gathered in Tab. 1 (see Figure 2 for identification of la-
bels). The examples indicate the feasibility of using MDL as
criterion. Label 128 is correctly selected as a building with
symmetric, sloped roof. Label 130 is classified as prismatic
model due to the fact that the roof consists of three gabels.
That is also true for label 126, but this building is classified
as having a symmetric, sloped roof, due to the fact that the
roof structure does not appear clearly in the DSM, because of
round off effects of the regularization in the DSM generation.
In all three cases, the difference in gain is significant. In such
cases, where the difference in gain is not significant, both
models should be regarded as possible alternatives and kept
for further processing.
Figure 5: FLAT: overlay DSM - ground plan (section)
5 RESULTS
In this section, some results of our approach are discussed us-
ing the ISPRS test data set FLAT with a ground resolution of
0.5m x0.5m and a DSM of a downtown area as examples. A
detailed description of the results of our approach for the IS-
PRS test data sets is given in [Weidner, 1995], also including
a discussion concerning the used control parameters. All re-
sults of this test have been compiled in [Sester et al., 1996].
A comparison between image and ground plan information
derived from the DSM for the data set FLAT indicates that
only one building has not been detected.
Bi ee LLLLVLLLLO is s t m d
