![](bg3.png)
more pale paths possible. Each newly sub-parts
formed are analysed in the same fashion till all the
cut-points are analysed for pale paths.
After analysing all the high concavity points, the
sub-parts are fed through morphological thinning
operation and again the X or T intersections are
checked. We already know whether an image
constitutes mainly of homologous chromosomes in
which sister-chromatid separation occurs (class A)
or does not (class B). In general, an X shaped
chromosome consists of 2 T-intersections or nodes
whereas a normal chromosome does not contain any
of them. Therefore, a sub-part with number of cut-
points greater than or equal to 2 is considered a
single chromosome, if it contains 2 or more skeleton
nodes for the image of class A or no node for the
image of class B. Any sub-part not complying with
this rule is tagged as overlap.
2.3.1 Pale Path Detection
We can categorize the cut-points into three different
types depending on their local convergent angles:
π/2, 3π/4 and π. The cut-point with convergent angle
π is resultant for close vicinity cut-points reduction.
All the cut-points are set to ‘0’ in the binary image.
For each of them, a 3x3 search is defined. Smallest
intensity within this window is then set to 0, which
is then used as the center of next iteration. The
iteration terminates only when the centre reaches the
boundary of object or the size of the search window
is reduced to 0.
An important point to note here is that the
iterative 3-pixel window search won’t always
provide the correct pale path. It will simply find a
path from one boundary end to another irrespective
of the intensity value traced. That may lead to
dissection of “cross-like” chromosome which would
result in false positive pale path. To overcome this
limitation, we classify the object further into high
intensity regions and pale regions. Only those pixels
which lie in the pale regions are searched for
minimum intensity in the 3-pixel window. If none of
the pixels of the window lie in the pale region, then
the search iteration is stopped, which indicates a
“cross-shaped” chromosome. The pale paths
detected for a group of 8 overlapping and touching
chromosomes is shown in Figure 2.
The classification into relatively high intensity
and pale regions is done by re-thresholding of the
object. The Otsu method applied to the object forms
a pale region that may contain the pale path as well
as a lot of the unwanted surrounding area. To avoid
this, we propose a novel method of classification
using the object’s image histogram.
It can be clearly seen that the pixels of grayscale
intensity less than the Otsu’s threshold plus an offset
can be subdivided into two regions: relatively high
intensity region comprising of chromosome bands
and relatively low regions comprising of pale paths.
In the envelope of the image histogram plot, we find
peaks corresponding to these two regions. Our aim is
to find the threshold around the minima to separate
the pale path region from the unwanted dark bands.
This is fulfilled by applying Intermeans Method on
the pixels less than the sum value of object’s Otsu’s
Threshold and the offset (set to 10) so that the search
window pixels are formed of grayscale intensity less
than the new threshold.
(a) (b)
Figure 2: (a) Binary image of a cluster of overlapping and
touching chromosomes. (b) The pale paths detected for
touching chromosomes.
For the case of class A type chromosomes, the
Intermeans method becomes inefficient because of
the large number pixels in the pale regions. To
compensate for this, Intermeans method is applied
only between the maxima of the two peaks of image
histogram. Hence, the reduced range of intensity
values increases the accuracy for this method.
The new threshold divides the object in a more
constricted pale region. A pixel in a search window
is applicable for search only if it lies in the pale
region obtained from the final threshold. When none
of the window pixels are a part of that region, the
search process stops.
2.4 Optimum Area Criterion
Sometimes, a small-sized extension of the
chromosome may split itself if it lies in the pale
region generated. To avoid such kind of anomalies,
we restrict the ‘pale-path splitting’ by an area
threshold. Only those sub-parts with a size more
than the area threshold can split to form a separate
chromosome. The area threshold is decided by
computing the mean and standard deviation (SD) of
the area of all the objects of binary image. Objects
with very large area are excluded, as they have a
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