The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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Image Domain 
Hough Domain 
Figure 4: Hough transformation. 
Points that lie on the same line in the image (feature space) will 
produce sinusoids that all intersect at a single point in the 
Hough domain (parameter space). For the inverse transform, or 
back-projection, each intersection point in the Hough domain is 
transformed into a straight line in the image (Figure 5). 
Figure 5: Example: Hough transformation. 
3. STRENGTHS OF THE HOUGH TRANSFORMATION 
3.1 Noisy Data 
The Hough transformation is a very powerful tool, especially 
when it comes to working with data sets that are noisy (IDL, 
2004). Figure 6 illustrates an example, where the original image 
consists of points lying on three lines. The second input image 
is identical but additionally salt-and-pepper (random) noise was 
added. In this image it is rather difficult for the human 
interpreter to recognize the original three lines. The next step is 
a transformation into Hough domain. For each point one 
sinusoidal curve is drawn. The intersections of the sinusoids 
characterize points lying on a common edge (in image space). 
The higher the amount of such common points on one line is, 
the more sinusoids intersect at the corresponding location in 
Hough domain. Then, the local maxima (of sinusoid 
intersections) are automatically detected by setting a threshold 
of 20. This means that it is searched for lines (in image space), 
on which at least 20 points lie. The found local maxima are then 
back transformed and the final outcome is in both cases 
identical. The noise was completely disregarded. 
Figure 6: Example with noisy data of Hough and back 
transform. 
3.2 Level of Detail 
Another big advantage is the level of detail that can be 
‘defined’ for the final back transformed building. It can easily 
be chosen how many edges (intersections of sinusoids in 
parameter pace =local maxima) should be back-projected into 
image space and used for the building-edge extraction. In 
Figure 7 an example with 6 and 15 back-projected edges is 
shown. 
Figure 7: Level of detail during the Hough Transformation. 
3.3 Forcing Angles 
Quite often buildings are characterized by certain geometric 
properties. For example, two walls intersect at a certain angle. 
In the building extraction process it may happen that this 
geometric property is lost, due to inaccuracies of the input data, 
inappropriate algorithm strategies or other sources of error. 
Despite that, we want the extracted building, to obey to these 
characteristics, so it represents reality in the best way. 
The implementation is quite easy, since the horizontal axis in 
parameter space represents angle 0. If the angle between two 
found edges has to be of a certain value, the horizontal distance 
between the corresponding local maxima in parameter space 
has to be equal to the wanted angle. Hence the deriving of the 
local maxima for the final back projection into image space is 
adjusted through the “angle” restriction (Figure 8). 
Also a tolerance value that describes how big the maximum 
deviation from the requested angle can be introduced so that it 
is still forced into the right position.