International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
in mind that since a conversion from a B-rep to a CSG rep-
resentation is ambiguous, deriving a CSG representation
from given (measured) data is ambiguous, too — unless ad-
ditional hints can resolve this ambiguity.
Looking at different modelling approaches, the following
points are of importance:
1. How is topological correctness of the surface en-
sured?
How are geometric constraints such as meeting sur-
faces, roofs of same slope, parallelism and rectangu-
larity enforced?
3. How is the desired level of generalization obtained,
i.e. which measures are taken to distinguish between
‘important’ parts that should be modelled and ‘unim-
portant’ parts, which have to be left away.
bo
When object representations are built using CSG, this
solves a number of issues. First, primitives themselves
are assumed to be topologically correct and Boolean op-
erations will preserve correctness. Second, geometric con-
straints hold for the primitives implicitly: for example, the
faces of a box are parallel or normal to each other. How-
ever, this does not extend by default to aggregates of prim-
itives. Third, by imposing limits on the allowed primitive
sizes, the generalization level can be controlled.
2 PREVIOUS WORK
2.1 Example Building Reconstruction Systems
This section reviews a selected number of building recon-
struction approaches with special focus on how they deal
with topological correctness, geometric constraints, and
generalization. Table 1 summarizes the main points.
(Haala and Brenner, 1997) derive a skeleton (Aichholzer
et al., 1995) from a given ground plan, which defines re-
gions of interest in the digital surface model (DSM). Ana-
lyzing these regions, roof surfaces are accepted or rejected,
and the skeleton is rebuild using only accepted surfaces.
The topological correctness is ensured by the skeleton al-
gorithm, which is constructive with well-defined result.
Geometric constraints are not imposed, which can lead to
wrong gable positions, especially when the ground plans
are displaced relative to the DSM. Since each ground plan
segment leads to at most one roof surface patch, the gener-
alization level is implicitly determined by the ground plan.
(Weidner, 1997) extracts roof faces using a DSM segmen-
tation. No topology is build. However, it is proposed to
automatically derive mutual relationships between the ex-
tracted faces, such as ‘same slope’, ‘symmetry’, and 'anti-
symmetry’, and to insert them as constraints into a global
robust adjustment. There is no control for the generaliza-
tion level except for the minimum accepted roof face size.
(Griin and Wang, 2001) extend a previous approach de-
scribed in (Griin and Wang, 1998). It is based on con-
ventional, manual measurement of corresponding image
1086
points in stereo images. For all vertices of the object to be
acquired, corresponding points have to be measured. The
resulting point cloud is termed “weakly structured”, since
the operator can give hints regarding the roof topology by
measuring in a certain order and placing the points in dif-
ferent layers. Then, an automatic process based on relax-
ation recovers the roof topology from the point cloud. Fi-
nally, constraints are formulated, e.g. all eaves points hav-
ing the same height, vertices of a face lying in a plane,
etc.. A least squares adjustment is used to estimate final
point locations. It seems that no constraints are used to
enforce relationships between different roof parts, as over-
lapping parts are corrected by a snap operation which is
done after the adjustment. Altogether, the approach builds
the surface of the object directly by a mixed manual and
automatic procedure. Regularity is enforced by some con-
straints as well as a snap. The generalization level is en-
tirely controlled by the operator.
(Gülch and Müller, 2001, Gülch et al., 1999) describe
an approach which is based on CSG primitives measured
semi-automatically in aerial images. Buildings are mod-
elled using a fixed number of parametric primitives like
flat-, desk-, saddleback-, hipped-roof etc., which are com-
bined by Boolean operations. The selection of each ap-
propriate primitive is carried out manually by an operator.
Then, the wireframe model is overlaid in two images and
the operator can adapt the parameters accordingly. The
adaption is supported by various image matching tools so
that only a few mouse clicks are necessary to instantiate
and measure a primitive. Topological correctness is en-
forced by the CSG approach. Regularity is enforced im-
plicitly by the primitives. Across primitives, a snapping
procedure is used. Generalization is controlled entirely by
the operator.
(Vosselman, 1999) extracts faces from non-regularized
laser scan data using a Hough transform, followed by con-
nected component analysis. From this, edges are found by
intersection of faces and analysis of height discontinuities.
No ground plans are used as additional information, how-
ever since jump edges cannot be determined very well from
laser scanning, a ‘main building orientation’ is derived and
used as a constraint for the edge orientation. The topology
is build by bridging gaps in the detected edges. The use of
geometric constraints is proposed. Generalization is again
controlled by a minimum face size.
(Brenner, 1999) divides ground plans into 2D primitives
(in this case, rectangles) using a heuristic algorithm. For
each of the 2D primitives, an optimal 3D primitive is se-
lected from a fixed set of available roof types, and its pa-
rameters are estimated using the DSM. The primitive se-
lection and parameters can be changed later on using a
semiautomatic extension. The final object representation
is obtained by merging all 3D primitives. Roof topology i$
generated by the Boolean merge operation. Adjacent 3D
primitives with similar eaves heights are ‘snapped’ to ex-
actly the same heights, however no constraints are formu-
lated and no combined adjustment takes place. The initial
2D primitive generation can be controlled by a buffer pa-
rameter which will omit primitives for small ground plan
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