Tr: how to compute central line form surface objects

[Adel Abdallah]

----- Original Message ----- 
From: Olivier Coulon 
To: Jan Ehrhardt 
Cc: vtk users 
Sent: Monday, February 21, 2000 2:28 PM
Subject: Re: how to compute central line form surface objects


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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