## Wednesday, October 24, 2012

### Contour : looking for negatively curved domains

A contour was previously explored with the convexity defects  algorithm implemented in opencv. Some highly curved domains  failed to be detected because of the contour shape.
 Curved domains missed by convexity defects detection

Using polygonal approximation imlemented in skimage 0.8 dev, positively curved domains as well as negatively curved domains on a contour can be sorted:
 Contour of a chromosomes cluster (blue), polygonal approximation (yellow). Red points: positive curvature. Yellow points: negative curvature.

From a segmented particle, a polygonal approximation of the contour is extracted.
Points of the polygon are used to compute an angle between two consecutive vectors:
$\alpha =\mathit{arg}\frac{{Z}_{\stackrel{⃗}{{A}_{n+1}{A}_{n}}}}{{Z}_{\stackrel{⃗}{{A}_{n-1}{A}_{n}}}}$
Positive angles correspond to convexe domains and negative angles to concaves domains.

The code has to be modified to filter angles according to a given range.

The code can be modified as follow to filter angles corresponding to curved domains:

• positive = table[(135>table[:,2]) & (table[:,2]>45)]
• negative = table[(-45>table[:,2]) & (table[:,2]>-135)]
 Curved domains on polygonal approximation of a chromosomes cluster contour.