how to compute central line form surface objects

[Olivier Coulon]

Jan Ehrhardt wrote:

> I have surface objects of anatomical tube-like structures (e.g.
> vessels)
> How can I compute a central line (the skelett) of a
> surface object ?
>
> Thanks.
>
>         Jan

Jan,

I think it is not a very simple problem. If your structure is a vessel, I
guess orthogonal sections are not exact circles and they are not even
exact ellipses. Therefore, the skeleton (in a morphological sense) is not
gonna be a line (it can be a "piece of surface", or several lines).
You can have a look at some kind of "medial axis" or "core" (see
"Computation of Object Cores from grey-level images", B.S. Morse, PhD
Thesis, University of North Carolina at Chapel Hill, 1994), but this not a
straightforward implementation in your case

If your surface is properly parameterised (i.e. one parameter r that goes
"along" the vessel, and one parameter s that goes "around" it, see the
figure below), you can get an approximation by computing for each value of
r the barycenter of the section described by s.  You'll then have a set of
points which more or less describe some kind of "central line", depending
on the quality of your parameterisation.


----------------------
       ^        -> r
       |s
----------------------

I guess that the problem is that it is not obvious to define what is the
"central line" of something which is not exactly a cylinder.

- Olivier


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