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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
a priori probabilities without training samples, which is
problematic if the assumption of a normal distribution of the
data vectors is unrealistic. We propose to use the theory of
Dempster-Shafer for data fusion, because its capability of
handling incomplete information gives us a tool to reduce the
degree to which we have to make assumptions about the
distribution of our data (Klein, 1999; Lu and Trinder, 2003).
1.2.2 Roof plane detection and delineation: Ameri and
Fritsch (2000) combined a DSM and aerial images for the
geometrical reconstruction of buildings by polyhedrons. They
searched for co-planar pixels in the DSM, which resulted in
seed regions for region growing in one of the aerial images. The
resulting roof planes were combined to form a polyhedral
model, which was then improved by fitting the model to image
edges. Problems were mainly caused by poor contrast, because
region growing was only applied to one of the aerial images,
and because the 3D information provided by the DSM was not
included in the region growing process.
Schenk and Csatho (2002) put forward the idea of exploiting
the complementary properties of LIDAR data and aerial images
to achieve a more complete surface description by feature based
fusion. LIDAR data are useful for the detection of surface
patches having specific geometrical properties and for deriving
parameters related to surface roughness, whereas aerial images
can help to provide the surface boundaries and the locations of
surface discontinuities. The planar patches detected in LIDAR
data are used to improve the results of edge detection in the
aerial images, and the image edges thus extracted help to
improve the geometrical quality of the surface boundaries.
Rottensteiner and Briese (2003) described a ‘method for roof
plane detection from LIDAR data, and they discussed strategies
for integrating aerial images in their work flow for building
reconstruction. They proposed to improve their initial planar
segmentation by adding new planar segments to the original
ones if sufficient evidence is found in the aerial images. They
also presented an adjustment model for wire-frame fitting. In
(Rottensteiner et al, 2003), we have shown how planar
segments can be detected by a combined segmentation of a
digital orthophoto and a DSM. In this work, we want to show
how the initial segmentation of the DSM can be improved by
matching the planar patches with homogeneous regions
extracted from two or more aerial images. This will result in
better approximations for the roof boundaries, and it will
support the distinction between roof plane intersections and step
edges (i.e. intersections between roof planes and walls). We
also want to show how the geometric quality of the step edges
can be improved using edges extracted from the digital images.
1.3 The Test Data Set
Our test data were captured in Fairfield (NSW), covering an
area of 2 x 2 km“. The LIDAR data were captured using an
Optech laser scanner. Both first and last pulses and intensities
were recorded with an average point distance of about 1.2 m.
We derived DSM grids at a resolution of 1 m from these data.
True colour aerial stereo images (1:11000, / — 310 mm) were
also available. These images were scanned at a resolution of
15 pum, corresponding to 0.17 m on the ground. A digital
orthophoto with a resolution of 0.15 m was created using a
DTM. Unfortunately, the digital images did not contain an
infrared band, which would have been necessary for computing
the NDVI. We circumvented this problem by resampling both
the digital orthophoto and the LIDAR intensity data
$13
(wavelength: 1064 nm) to a resolution of 1 m and by computing
à "pseudo-NDVI-image" from the LIDAR intensities and the
red band of the digital orthophoto.
In order to evaluate the results of building detection, a reference
data set was created by digitising building polygons in the
digital orthophoto. We chose to digitize all structures
recognisable as buildings independent of their size. The
reference data include garden sheds, garages, etc, that are
sometimes smaller than 10 m? in area. Neighbouring buildings
that were joined, but are obviously separate entities, were
digitized as separate polygons, and contradictions between
image and LIDAR data were excluded. Thus, altogether 2337
polygons could be used for evaluation.
2. BUILDING DETECTION
The input to our method for building detection is given by three
data sets. The last pulse DSM is sampled into a regular grid by
linear prediction with a low degree of filtering. The first pulse
DSM is also sampled into a regular grid, and by computing the
height differences between these DSMs, we obtain a model of
the height differences between the first and the last pulses
AH py. The normalised difference vegetation index (NDVI) is
computed from the near infrared and the red bands of a
geocoded multi-spectral image (Lu and Trinder, 2003).
The work flow for our method for building detection consists of
two stages. First, a coarse DTM has to be generated. We use a
hierarchic method for DTM generation that is based on
morphological grey scale opening using structural elements of
different sizes (Rottensteiner et al., 2003). Along with cues
derived from the other input data, the DTM provides one of the
inputs for the second stage, the classification of these data by
Dempster-Shafer fusion and the detection of buildings. Five
data sets contribute to a Dempster- Shafer fusion process
carried out independently for each pixel of the image containing
the classification results. After that, initial building regions are
instantiated as connected components of building pixels, and a
second fusion process is carried out on a per-building level to
eliminate regions still corresponding to trees.
2.1 Theory of Dempster-Shafer Fusion
This outline of the theory of Dempster-Shafer is based on
(Klein, 1999). We consider a classification problem where the
input data are to be classified into » mutually exclusive classes
C; € 0. The power set of 0 is denoted by 2^. A probability mass
m(A) is assigned to every class A € 2° by a “sensor” (a
classification cue) such that m(&) = 0, 0 € m(A) < I, and
2 m(A) = 1, where the sum is to be taken over all A € 2% and ©
denotes the empty set. Imprecision of knowledge can be
handled by assigning a non-zero probability mass to the union
of two or more classes C;. The support Sup(4) of a class 4 e 2?
is the sum of all masses assigned to that class:
Sup(A) = > m(B) (1)
Bc A
Sup( A) is the support for the complementary hypothesis of A:
An Ä = 6 Sup( A ) represents the degree to which the
evidence contradicts a proposition, and it is called dubiety. If p
sensors are available, probability masses m;(B;) have to be
defined for all these sensors i with / X i € p and B; e 2^. The
