Touching chromosomes, overlapping chromosomes, single chromosomes and their convexity defects

Let's start with convexity defects (blue circles) detected in totally overlapping chromosomes:

The convexity defects can be directly used to resolve the two overlapping chromosomes, the script is used with d>1000 (see the two previous posts).

When the chromosomes partially overlap, we can have less than four points detected:

As in the previous post, touching chromosomes produce convexity defects. In the following example of two small chromosomes, the two convexity defects detected surrounds the "touching region" . Tracing a segment between the two points would cut the particle (green contour) into two complete chromosomes.

 However touching chromosomes do not always produce  "good" pair of convexity defects which could be used to separate them. In the two following examples, we have two kinds of convexity defects (CD): CDs closed to the touching domain (at coordinates:grossly [30;20] or [40;75] )and CDs near the  centromere (coordinates [35;60]).

Two CDs near the centromere, one CD near the touching region.

Two CDs around the touching region, one CD near the centromere

 In the following cluster of four human chromosomes, only CDs corresponding to the three touching domains were detected. Note that a point at (50,80) corresponding to a touching domain in a highly bended part of the contour and quit far from the convex hull (red) was not detected:

Convexity defects are also detected on single chromosomes keeping the same parameters (d>1000). Let's start with two good cases where the pair of CDs are around the centromere:

The chromosome morphology can alter the detection:

In all the previous example, only CDs with d>1000 were kept. Lowering the  threshold for the d value increases the number of CDs, here is some examples with single chromosomes:

Probably HSA2 chromosome: d>100 : Two CDs are close to the centromere, the others are false positive CD

d>500 : one false positive CD for centromere detection

d>1000 : only one CD near the centromere is detected

For a smaller chromosome (may be chromosome 17), we get:

CD with d>1000

CD with d>500