Thë International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
4.1.3 Features: Three types of features were extracted from 
the data: 
- height difference between the first pulse laser DSM and 
the last pulse laser DSM (DSMfe-DSMle); 
height difference between the last pulse laser DSM and 
the DTM (DSMle-DTM); 
- Normalized Difference Vegetation Index (NDVI) derived 
from the red and near infrared image channels. 
In the Bayesian approach, the extracted features were directly 
used for evaluating the decision function. To compute the 
mean and covariance matrix for each class a set of training 
regions was specified in the data. Fig. 2.A shows the training 
regions. 
In the Dempster-Shafer approach, features were used to obtain 
evidence (probability mass) for each class hypothesis. For the 
derivation of evidence we developed linear evidence 
assignment functions based on the training data. These 
functions were tuned by trial and error to yield best separation 
of the objects. Fig. 3 illustrates the evidence assignment 
functions. 
The combination of evidences derived from different features 
was carried out using the combination rule given in Eq. (6). 
Table 1 and Table 2 demonstrate the evidence combination 
process where s is the evidence derived from the height 
difference between the last pulse DSM and the DTM, t is the 
evidence derived from the height difference between the first 
and last pulse DSMs, and u is the evidence derived from the 
NDVI. Table 3 summarizes the final evidence values 
computed for the four classes. 
Both the Bayesian and Dempster-Shafer methods were applied 
in pixel level and in object level. In pixel level, features and 
evidence values were computed for each individual pixel. In 
object level, a segmentation of the color infrared orthoimage 
was first obtained, and the mean of features within each 
segment was used in the computations. The segmented 
orthoimage is depicted in Fig. 2.B. As can be seen, the image 
is slightly oversegmented so that overgrown regions are 
avoided. 
4.1.4 Detection of buildings: As mentioned before, 
buildings are the main object of interest in this research. 
Therefore, to evaluate the performance of the fusion methods in 
the context of building detection a binary building image was 
obtained from the classification results. A morphological 
opening operation was applied to clean this binary building 
image from small objects that were identified as building. This 
process was followed by a morphological reconstruction 
operation to retrieve the building boundaries that were 
smoothed out in the opening process. Fig. 4 illustrates the effect 
of this post-processing in a sample binary building image. 
4.2 Results 
The Bayesian and Dempster-Shafer methods were applied to 
the data in both pixel level and object level. In the application 
of Bayesian maximum likelihood method, we noticed that, the 
variance of the height difference between the first and lust pulse 
laser data in the building training regions was considerably 
small. To examine the influence of small variance, and 
consequently nearly singular covariance matrix, we also 
classified the data with the minimum distance method. Fig. 5 
shows the classification results as well as the detected buildings 
obtained by applying the three methods to the data in pixel level. 
Fig. 6 shows the object-level results. As can be seen, the three 
methods yield slightly different classifications of the data in the 
four predefined object classes methods; however unlike the 
Bayesian maximum likelihood and minimum distance methods, 
the classification results of the Dempster-Shafer method include 
also pixels and objects that are not assigned to any of the four 
classes (shown in black in the lower left images of Fig. 5 and 
Fig. 6). For the evaluation, these unclassified pixels were 
considered not-building. 
A В 
Fig. 1. A. Color infrared aerial orthoimage of the study 
area; B First pulse laser range image of the 
area. 
Building Tree Land Grass 
Fig. 2. A. Training regions for four classes; B. Segmented 
CIR orthoimage. 
The evaluation of the performance of the methods was carried 
out based on a set of ground truth data that contained building 
boundaries extracted manually from the RGB orthoimage. Fig. 
7 depicts these reference building boundaries. Three 
performance measures were obtained by comparing the 
buildings detected using each method and the reference data: 
- Detection rate: the ratio of the number of pixels correctly 
detected as building to the total number of building pixels 
according to the reference data; 
- False positive: the ratio of the number of pixels wrongly 
detected as building to the total number of not-building 
pixels according to the reference data; 
- False negative: the ratio of the number of pixels wrongly 
detected as not-building (missed building pixels) to the 
total number of building pixels according to the reference 
data.