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The algorithm involves expensive computation, but it has the advantage of produc-
ing acceptable segmentation results independently of the kind of image. In fact, the
approach followed in [17] rather than identifying the watershed lines during the Wa-
tershed Transformation, first builds the complete partition of the image into basins
and only after that detects the watershed lines by boundary detection. In this way,
both drawbacks affecting the Vincent-Soille approach are overcome at the expense of
higher computation costs. Therefore, neither the Frucci algorithm presented in [17],
nor the extension of the Frucci algorithm introduced in [10], are suitable for real-time
processing.
We have used the new implementation of the algorithm [10], [11] for our case-
based reasoning studies, since the computation costs are much lower then, due to the
use of the Watershed Transform computed by the Vincent and Soille scheme.
Let X and Y be two adjacent basins in the watershed partition of a grey-level image
D and W and Z some other basins. As in [17], we denote
LO , the local overflow of
X with respect to Y , as the pixel with the minimal grey value along the border line
between X and Y . The value of the pixel with the lowest value is the overflow of X,
O . Furthermore,
XY
R
is the grey value of the regional minimum of X ,
X
SA
=−
R
R
D OR
=
denotes the similarity parameter and
defines
XY
X
Y
XY
XY
x
LO (see Fig. 14).
In order to determine if a basin X has to be merged with a basin Y , Frucci et al.
[10] introduce the notion of relative significance of X with respect to Y and perform
the following check.:
the relative depth of X at
XY
1
2
SA
D
abT
,,
0
a
XY
+
b
XY
T
, with
(5)
At
Dt
where At and Dt are the threshold value (for the automatic computation see [17]) a, b
and T constants, and the left side of 5 is the relative significance of X with respect to Y .
Fig. 14. Similarity parameter and relative depth
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