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If condition 5 is satisfied, the basin
X
is significant with respect to
Y
. The relative
significance f
X
is evaluated with respect to all its adjacent basins. Three cases, as
shown in Table 1, are possible. When merging is possible, Table 1 also specifies if
digging or flooding has to be performed. After flooding or digging have been
performed for all basins that are not strongly significant, the Watershed Transforma-
tion is executed again with an obviously smaller number of local minima.
Table 1.
Cases for the significance of
X
by taking into account the relative significance with
respect to all its adjacent basins
X
is denoted
if
type of merging
strongly
significant
X
is significant with respect to each
adjacent region
Y
.
no merging
non
significant
X
is non-significant with respect to
each adjacent region
Y
.
flooding
partially
significant
all other cases
digging
Flooding:
All the pixels
of
X
with a lower grey value than
O
are set to the value
O
. If Watershed Transformation is executed again, the basin
X
results to be merged
with any adjacent basin
Y
for which the value of
LO
is
O
.
Digging:
The basin
X
is only merged with any adjacent basin
Y
, being non- signifi-
cant with respect to
X
and in such a way that
XY
R
≥
R
. Therefore, a canal is dug from
X
Y
LO
the regional minimum of
X
to the regional minimum of
Y
passing through
. All
XY
the pixels of the canal whose grey values are greater than
R
are set to
R
.
We have implemented the segmentation algorithm [10] by computing the Water-
shed Transform according to the scheme of Vincent and Soille, so as to reduce the
overall computation cost. However, using such a watershed model creates some prob-
lems due to the fact that watershed lines may be missing or thick, which inhibits in
A A A A W
A A A W B
W W W B B
W W W W B
W W W W W
(c) Result basin A and B
and watershed lines
6 6 6 6 32
6 7 7 32 0
13 13 12 3 0
8
6 6 6 6 32
6 6 7 32 0
13 13 12 3 0
12 12 12 32 0
12 12 12 12 32
(b) Result after flooding
8
8
32
0
8
8
8
8
32
a) Portion of an image
Fig. 15.
Successive results for an image after flooding and Watershed Transformation based on
the Vincent-Soille algorithm
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