Meta-learning for Image Processing Based on Case-Based Reasoning - Computational Intelligence in Healthcare: Advanced Methodologies - page 227

(a) Original image
(cross has one pixel
width)

(b) Segmentation
results of (a)

(c) Result for a 90°
clockwise rotated
image of (a)

(d) Result for a 90°
counterclockwise
rotated image of (a)

Fig. 11. Cross image and segmentation results using the Vincent-Soille algorithm (4-connected)
for rotated images

(a) Original image - a two pixels wide cross (b) Result using Vincent-Soille algorithm

(4-connected)

Fig. 12. A scaled image and the segmentation result using the Vincent-Soille algorithm
(4-connected)

This property also explains why the algorithm is not invariant with respect to rota-
tion (see Fig. 11) and scaling (see Fig. 12).
The cross in image Fig. 12 has double the width in comparison with the cross in
Fig. 10. The light-colored pixel at the intersection of the light-colored and dark-
colored branches of the cross has now only two darker neighbors. In such a condition
we obtain the correct result for the Watershed Transformation.
Scaling algorithms generally use interpolations, which can produce more regional
minima in the rescaled image than in the original image. As a consequence, a larger
number of components can be obtained for the scaled image, which will result in a
different segmentation from that of the original image.
The Vincent-Soille algorithm does not generate always connected watershed lines.
A reason for that is the constraint demonstrated in Fig. 6. No watershed line separates
the two basins A and B, if all the highest grey pixels between the two basins belong to
the geodesic influence zone of either A or B. For example, consider Fig. 13 (a), show-
ing an image completely black except for a grey stripe that is four pixels wide. For
this image the Vincent-Soille algorithm creates no watershed line between the two
basins, because no pixel of the stripe has the same distance to the two basins (com-
pare Fig. 13b and c).
To solve the two above drawbacks, Roerdink and Meijster [8] proposed a slightly
modified algorithm, which is, however, remarkably more expensive with regard to