In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. 1APRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009
85
y.
p
H(0,p)
paK. ►
\ 8
À 6
jt/2
X
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.
