Manfred H. Günzl
Figure 5: The well known image of Lena Soderberg (a) reduced to 1000 segments minimizing the variance (b), multiplied
with 7, (C) and multiplied with a aspect ratio compensation (d).
whereas the error of non exclusive coverage is given by
S card(P; f) Si)
T Si card(S;) !
Where card(S) is the number of members of the set S. As a total measurement of quality the sum e :— e, 4- e; of these
two kinds of errors were taken. The application of extracted speckle on idealized data enables the analysis of data with a
different signal to speckle ratio. In case of SAR data, n-look images with uniform resolution can be simulated using data
from one single flyover.
e5:m1
A region growing by merging algorithm keeping track of the parameters needed to derive Toe, Was implemented. Starting
with every single pixel as a region with four neighboring regions, a recursive merging is applied. Storing neighborhood
relations along with the geometric parameters P, E, C and the pixel coordinate sums and square sums within a binary
heap data structure (Cormen et al., 1990, 7.1) enables a computationally efficient continuous update of 7,,,, during the
segmentation process. Using this heap data structure the computational effort for a segmentation of a P x q image matrix is
of the order O(pq ld(pq)). The canonic region growing approach without the shape parameter is shown in fi gure 6(d) with
e = 0.88. The merging criterion was to minimize the standard coefficient of variation (SCV) (Beaulieu and Goldberg,
1989, Tilton and Cox, 1983, Tilton and Ramapriyan, 1988). The SCV was taken instead of the variance because of
multiplicative character of the speckle effect. Applying the shape parameter just by multiplying the SCV and z,,,. similar
to the Lena image example leads to very bad results with e — 0.96 as shown in image 6(e). Never the less extensive tests
with different combination operators and weighting parameter showed that even in this case the shape parameter is able to
356 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
