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2 0 2
0 1 0
2 1 2
W B W
A W C
A W C
W B W
A C C
W C C
(a) Original image
(b) Result by using theoretical
recursion (4-connected)
(c) Result by using Vincent-
Soille (4-connected)
Fig. 8. Comparing the results of the theoretical recursion with Vincent-Soille algorithm under
condition 2
schemes introduces some drawbacks. Specifically, watershed lines thicker than just
one pixel can be created and differently labeled basins (see Fig. 7). A pixel that be-
comes during an iteration t the watershed label and is neighbor of 2, 4, or more odd-
numbered pixels with different labels, can get the wrong label during the same itera-
tion after having visited all adjacent basins (see Fig. 8).
Another example of thick watershed lines created by the above modification is
shown in Fig. 9.
(a) Image
(b) Result (red: Watershed lines)
Fig. 9. A segmentation result using the Vincent-Soille algorithm (4-connected)
Theoretically, the results of the Watershed Transformation do not depend on the
order in which the neighbors of a pixel are visited. Because of the constraints intro-
duced by Vincent-Soille into the implementation of the algorithm, the order of visita-
tion heavily influences the result. For example, if for a pixel (, )
xy its neighbors are
{
}
visited, in the order
(
x
1, ,(,
y
xy
+
1 ,(
x
+
1, ,(,
y
xy
1)
(see Fig. 10b), or in the
{
}
order
(
xy
,
+
1), (
x
1,
y
), (
xy
,
1), (
x
+
1,
y
)
(see Fig. 10c), different results will
be obtained.
(a) Original image (cross has
one pixel width)
(b) Result with pixel visiting
order 1
(c) Result with pixel visiting
order 2
Fig. 10. Cross image and segmentation results using the Vincent-Soille algorithm (4-connected)
when different pixel visiting orders are used
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