how to compute central line form surface objects

[Jan Ehrhardt]

Oliver,

yes it´s not properly defined what is the "central line". But
I hope everyone knows what I mean. 
I have the suggested r parametrization implcitly in a special
case: For surfaces of long-bones constructed from CT data 
I can use the z-coords as r. Well maybe this will work.
I remember an equivalent problem:
How to compute the way of camera in virtual 
(gastro-intestinal or bronchial) endoscopy ?

Maybe anyone else has done this ??

Jan


Olivier Coulon wrote:
> 
> 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
> 
> 

-- 
-----------------------
Jan Ehrhardt
mailto:ehrhardt at medinf.mu-luebeck.de
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