ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
160 T T T T T T
140} -
100r A
60r
40 i
20r 4
0 L L L L L L L
220 225 230 235 240 245 250 255 260
Zz
Figure 2: Likelihood of building location
be able to deal with small height variations, there is no need to
check every individual height value. If these height values can
be grouped in small intervals then it suffices to check a value
from each group. Therefore a k-nearest neighbor algorithm
is applied for creating clusters of height values. The value
of k is determined by according to the variations that can be
handled by the reconstruction procedure.
For the building from Figure 1 by thresholding we get 7 height
values. These 7 values can be further reduced to 4 clusters
of height values by applying k-nearest neighbor classification.
The height corresponding to the highest value of each cluster
is used to generate some building hypotheses which are going
to be verified by fitting them to image data. Hence the lo-
calization of the building in the image will only be completed
when the correct building model is found.
4 GENERATION OF BUILDING HYPOTHESES
4.1 Library of Building Primitives
Most buildings can be described as aggregation of simple
building types. Starting from this observation, the knowledge
about the problem domain can be represented in a building
library containing the simple building models. As basic build-
ing models, we can consider a flat roof, a gable roof and a
hip roof building. The approach of modelling buildings using
a set of basic building models (primitives) suggests the usage
of CSG representation for building description. In this way,
a complex building can be seen as a CSG tree, where the
leaf nodes contain primitive building models and the internal
nodes contain boolean operations such as union, intersection,
difference. The basic building primitives of the CSG represen-
tation can be described by parametric models having shape
and pose parameters.
The first of the primitives is a flat roof building (Figure 3a).
A rectangular volume encodes the geometrical properties of
this type of building. To describe a flat roof building primitive
6 parameters are necessary: 3 shape parameters and 3 pose
parameters. The shape parameters are: width (w), length (1),
height (h). The pose parameters are: x, y coordinates of the
buildings’ reference point and the orientation in the xy-plane.
The height h is actually the sum of the height of the terrain
Figure 3: Parametric building models a) Flat roof building
b) Symmetrical gable roof building c) Non-symmetrical gable
roof building
and roof.
Another primitive is a symmetrical gable roof building com-
posed from a rectangular volume and a triangular volume
(Figure 3b). Therefore, for a gable roof primitive an extra
parameter, the height of the ridge has to be added to the
parameters of a flat roof primitive.
A more general gable roof primitive, the non-symmetrical
gable roof has an additional parameter the distance from the
roof reference point to the ridge base point (Figure 3c).
4.2 Fitting of Building Models
To find the best fit of an instance of a building model to an
image, we must find the shape parameters and the position
parameters, which best match the model to the image. This
can be done using a fitting algorithm.
The approach for fitting 3D building models to an image is
based on projecting the model into the image and finding the
parameters of the model that maximizes some measure of
the goodness-of-fit between model projection and image. In
most cases it is possible to solve for all unknown parameters
of a building model from matches to a single image. However,
the accuracy of the parameter estimation can be substantially
improved by simultaneously fitting the model to images taken
from different viewpoint. The method presented here can
be used in either situation. This method is a modification
of Lowe's fitting algorithm [Lowe, 1991]. It was developed
by Vosselman and used for semi-automatic reconstruction of
3D buildings [Vosselman and Veldhuis, 1999] and industrial
piping installation [Ermes, 2000].
The application of this fitting algorithm requires approximate
values for the model parameters. These approximate values
can be obtained from the map and from images.
In the initial approximation the x, y coordinates and the ori-
entation of a building primitive are given by the ground plan
of the building. The width and length parameters are the
width and the length of the rectangle corresponding to the
ground plan of the building partition. The height is given by
the localization procedure. In case there are more possible
heights, then a fitting is done for each of them.
A - 358
