Digital Signal Processing Reference
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intuitive idea can be visualized in geographical terms: in a landscape
flooded by water, watersheds divide the domains of attraction of rain
falling over the region. If image properties are measured by a single
variable specified at each pixel, the watershed algorithm finds connected
components belonging to separate local minima. This algorithm was first
proposed by Digabel and Lantuejoul [68] and later improved by Beucher
and Lantuejoul [32]. A nice up-to-date overview can, for example, be
found in [222]. More elaborate frameworks and extensions have been
proposed, such as the combination of watershedding with region merging
in a hierarchical structure [107] or graph-theoretic segmentation known
as the n -cut method [231].
An application of the watershed transform to cell image segmenta-
tion and recognition is presented in [191]; however, the cell images are
acquired from bone marrow smear, which substantially reduces back-
ground noise. Furthermore, no focusing problems are involved, so all
cells are of similar shape, texture, and especially size.
A more direct method, which has recently been suggested for slice
image segmentation in [30], uses thresholding for noise removal, and
afterward simply counts the number of connected components. Clusters
of appropriate pixel size are then interpreted as a single cell and counted.
We have also considered the use of these more classical approaches
to cell counting, but apart from some computational issues (and choice
of the various involved thresholding parameters), the main disadvantage
in contrast to the proposed algorithm lies in the fact that the above algo-
rithms do not take the actual cell shapes into account. Essentially they
are indifferent to shape, and count any object of appropriate color and
pixel size. A related problem can be seen in figure 13.9. There compare
ZANE with the two most common methods by applying the watershed
transform both to the confidence map and to a distance map (containing
distance values of pixels to cell boundaries given by a threshold). In both
cases the result strongly depends on image preprocessing and thresh-
olding to avoid too many local minima. Apart from some misclassified
regions due to thresholding problems, watershedding of the confidence
map partially separates cell clusters, but also introduces additional seg-
ments at intersections. If water shedding was applied to the distance
map, cell clusters could not be separated at all. We believe that this is
due to the somewhat problematic conditions of image acquisition using
a confocal light microscope, which cannot give cell boundaries as clearly
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