ISPRS Commission III, Vol.34, Part 3A ,,Photogrammetric Computer Vision", Graz, 2002 
  
3.2. Region Elevation Measurement 
The second attribute assigned to the roof regions quantitizes 
the height of each region (RH), Equation 2. A digital 
elevation model is used for this task. First each point in the 
image is assigned an elevation value by projecting the DEM 
back to the image using the image registration information, 
the pixel location in the image, and the DEM. For each 
image point a ray is generated starting from the exposure 
station of the camera and is directed toward the point. The 
intersection between the ray and the DEM defines the 
elevation of the image point. The RH is measured as the 
percentage of the number of the roof region points that are 
above a certain elevation to the total number of points in the 
region. 
RH = Number of Region Points Above H min Q) 
Total Number of Region Points 
  
Where H = Min Building Elevation 
3.3. Implementing the Neural Network 
Figure 3 shows a 2D plot for the two region attributes, the 
total number of regions is 2081 regions, 623 regions are roof 
regions and the rest are non-roof regions. A simple two- 
layered Neural Network is used to discriminate between roof 
and non-roof regions, Figure 4. The activation function for 
all nodes is the Sigmoid Function, (Principe ef. al., 1999). 
  
  
  
  
me 108 
P L3 
  
  
Figure 3. Scatter Diagram of Border Linearity (BL) vs. 
Region Height (RH) 
  
  
Figure 4. The Implemented Two-layered Neural Network 
To study the performance of the Neural Network a variety of 
training data sets were used with different sizes. The training 
data set sizes used are 20, 50, 100, 200, and 400 samples. For 
each training data set size the experiment was performed 10 
times using a non-overlapping randomly selected training 
data set. The average detection rate and false alarm rate for 
each training data set size is recorded and shown in Figures 
5-and b. 
100 
  
99.5 4 
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Detection 
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zn) 2i 100 200 A400 
duy - 
Furber o£ Traming Samples 
Figur5-a. The Detection Rate vs. Training Data Set Size 
  
  
  
  
12 
10 « 
23 
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a 
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Number of Training Samples 
Figure 5-b. The False Alarm Rate vs. Training Data Set Size