The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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buildings if they have the same height as buildings. A height 
model of the scene can also be generated using an airborne laser 
scanner. Vosselman,(1999) uses laser scanner data to generate a 
Delaunay triangulation to reconstruct the rooftops and thus the 
buildings. 
With the availability of multi-source aerial data in recent years, 
data fusion approaches to building detection have increasingly 
attracted attention. One of the common approaches to data 
fusion for classification of objects is based on the Bayesian 
decision theory. Walter,(2004) applies Bayesian maximum 
likelihood method to object-based classification of multi- 
spectral data. Rottensteiner et al.,(2004b) fuse height data with 
NDVI from multispectral images based on Dempster-Shafer 
theory. Lu et al.,(2006) use a similar method to detect buildings 
in multi-source aerial data based on the Dempster-Shafer theory. 
3. BAYESIAN AND EVIDENCE-BASED DATA FUSION 
FOR BUILDING DETECTION 
3.1 Bayesian approach 
In a typical data fusion strategy, feature vectors are extracted 
from the multi-source data, and a decision is made for each 
feature vector as to what class of object it belongs to. In the 
Bayesian fusion, a decision is made on the basis of maximizing 
the likelihood of a feature vector x being belonged to a class Wj. 
This is realized by evaluating a decision function for each 
feature and each class (Duda et al., 2001): 
dj (*) = p{x/ Wj ) • P(Wj ) (l) 
where the conditional probability pjx/wf is the probability of a 
feature vector x when drawn from the class Wj, and P(wf) is the 
prior probability of the class Wj. The pixel or object with the 
feature vector x is then assigned to the class vv, if: 
dj(x) > dfx) Vi*j (2) 
classes. Accordingly, the method is referred to as the minimum 
distance classification. 
3.2 Dempster-Shafer approach 
Dempster-Shafer data fusion approach is based on making 
decisions according to available evidence for each object class. 
Each feature is seen as a piece of evidence that provides a 
certain degree of belief in each class hypothesis (Gordon and 
Shortliffe, 1990). Hypotheses include not only all classes but 
also any union of the classes. The effect of a piece of evidence 
to the hypotheses is represented by a probability mass 
assignment function m. The amount of belief to a hypothesis A 
is represented by a belief function: 
Bel(A)=Y, m (B) (5) 
BqA 
which is the sum of the mass probabilities assigned to all 
subsets of A by m. When two or more evidences are available, 
the probability masses assigned to the hypotheses are combined 
using the following combination rule: 
m(zl) = 
i,j 
B,r\Cj=A 
1 ~k 
(6) 
where 1-A: is a normalization factor in which k is the sum of all 
non-zero values assigned to the null set hypothesis 0. The 
decision on the class of a feature can be made based on a 
maximum belief decision rule, which assigns a feature to a class 
A if the total amount of belief supporting A is larger than that 
supporting its negation: 
Bel(A) > Bel (A) (7) 
4. EXPERIMENTS AND RESULTS 
The probabilities in Eq. (1) are derived from the training data. 
Feature vectors are often assumed to have a Gaussian 
distribution; thus, pjx/wf is replaced with a multi-dimensional 
Gaussian function with parameters p and I (mean and 
covariance respectively). The decision function can then be 
expressed as: 
dj(x) = ~ (* -“PjÏ ~\ lo s|X, 1 + logPOv,) (3) 
Classification of features based on the decision function given 
in Eq. (3) is referred to as the maximum likelihood method. A 
simple case of the maximum likelihood method is when an 
assumption can be made that the features in all classes are 
independent and have the same variance. Further, if it can be 
assumed that the prior probabilities of all classes are the same, 
the decision function in Eq. (3) will simplify to: 
dj(x) = -^(x-jUj) T (x-Pj) (4) 
which suggests that instead of maximizing the decision function, 
a classification of feature vectors can be performed on the basis 
of minimizing the distance of each feature to the means of the 
4.1 Experimental setup 
Experiments were conducted to evaluate the performance of the 
Bayesian and evidence-based fusion in building detection. The 
study area was a suburban part of the city of Memmingen, south 
of Germany. 
4.1.1 Data: The available data for the experiments included 
airborne laser range data containing first pulse and last pulse 
DSMs with a density of 1 point per m 2 , and orthorectified aerial 
imagery in visible and near infrared channels with a ground 
resolution of 0.5m. In addition, a DTM of the scene was 
available in which buildings and other objects were filtered out. 
Fig. 1 depicts the color infrared orthoimage and the first pulse 
laser range image of the study area. 
4.1.2 Classes: For the classification of objects in the study 
area four classes were considered: building (B), tree (T), bare 
land (L) and grass (G). The main object of interest was building, 
and in the final evaluation only buildings were taken into 
account.