In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. 1APRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009 
85 
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p 
H(0,p) 
paK. ► 
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Image Domain 
Hough Domain 
Figure 4: Hough transformation. 
Points that lie on the same line in the image (feature space = 
Image Domain) will produce sinusoids that all intersect at a 
single point in the Hough domain (parameter space = Hough 
Domain). 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. 
The research shows that by using the Hough Transformation for 
building extraction we have many advantages, such as the good 
handling of noisy data, the easy adjustment of level of detail of 
the output data, the ability to force certain geometric properties 
into the extracted buildings and the possibility to bridge gaps, 
meaning that building comers that might not be visible in the 
imagery can be determined accurately. The proposed 
methodology proves to have certain weaknesses when dealing 
with radiometrically heterogeneous roofs, when big shadows 
cover large areas of roofs of the buildings to be extracted, when 
the building geometry becomes very complex, or when the 
input data set comprises many compound building (Vozikis and 
Jansa, 2008). 
2.2 Image Matching 
This strategy follows the basic principle of image matching by 
correlation. A given reference image matrix is searched in the 
image under investigation (the so-called search image) by 
moving the reference matrix pixel by pixel over the entire 
image area. Potential candidate positions, i.e. positions of high 
similarity, are marked if a so-called correlation coefficient 
exceeds a predefined threshold. In order to find the optimum 
geometric fit, the searching procedure includes, besides 
translation, also rotation and scaling. Thus houses of similar 
shape but different size are found too. 
The reference image is usually a small image matrix, here 
depending on the size of the building to be searched, whereas 
the search image is a rather big image matrix in our case 
covering the whole area under investigation. 
Figure 6: Search, reference and correlation image. 
Figure 6 shows the principle of the correlation procedure. The 
left hand side indicates the searching process with the reference 
image and the given spacebome or airborne image as search 
image. The correlation index is computed for each position of 
the reference image and the results are stored as similarity 
measure in the so-called correlation image. Potential building 
positions are characterized by a high correlation coefficient and 
thus the correlation image just needs to be thresholded and the 
local maxima are localised. It has to be mentioned that one 
crucial parameter is certainly the appropriate threshold value. 
Its choice determines quite significantly the quality of the 
result. If the threshold is too low, too many buildings are 
detected leading to a great number of false matches. If the 
threshold is too high, the selection is too strict and, as a 
consequence, too many buildings will be rejected. It is not 
possible to define an optimum threshold as a general 
suggestion. For the cross-correlation coefficient using 0.7 to 0.8 
is certainly a good choice for starting, but individual 
adjustments are necessary in any case. 
As measure of similarity the cross-correlation coefficient 
(Equation 3) is adopted, but also other measures can be used 
(Equations 4 and 5). 
Z(i. - £iMs2 -£2) 
(3) 
VZta -ii)-X(s2 -fj) 
Ek -SiKsi +#2)) 
(4) 
lE(g, -82f 
(5) 
C > = ll » 
where gl and g2 are the grey values in the reference and search 
window, 
£'and £2 are the mean grey values in the reference and the 
search window and 
n is the number of used pixels. 
Kraus (1996) suggests rewriting Equation 3 as follows for a 
more efficient computation: 
'g; -»-fi 1: (6) 
Vl(*r - n ■ g; )■ Z U: - « • f ? ) 
Note, that when using Equation 6 the computing effort is 
reduced since the expression w ) is constant during 
the whole process and has to be calculated only once.