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<DIV style="FONT: 10pt arial">----- Original Message -----
<DIV style="BACKGROUND: #e4e4e4; font-color: black"><B>From:</B> <A
href="mailto:o.coulon@cs.ucl.ac.uk" title=o.coulon@cs.ucl.ac.uk>Olivier
Coulon</A> </DIV>
<DIV><B>To:</B> <A href="mailto:ehrhardt@medinf.mu-luebeck.de"
title=ehrhardt@medinf.mu-luebeck.de>Jan Ehrhardt</A> </DIV>
<DIV><B>Cc:</B> <A href="mailto:vtkusers@public.kitware.com"
title=vtkusers@public.kitware.com>vtk users</A> </DIV>
<DIV><B>Sent:</B> Monday, February 21, 2000 2:28 PM</DIV>
<DIV><B>Subject:</B> Re: how to compute central line form surface
objects</DIV></DIV>
<DIV><BR></DIV>Jan Ehrhardt wrote:
<BLOCKQUOTE TYPE="CITE">I have surface objects of anatomical tube-like
structures (e.g. <BR>vessels) <BR>How can I compute a central line (the
skelett) of a <BR>surface object ?
<P>Thanks.
<P> Jan</P></BLOCKQUOTE>
<P><BR>Jan,
<P>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). <BR>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
<P>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. <BR>
<P><TT>----------------------</TT> <BR><TT>
^ -> r</TT>
<BR><TT> |s</TT>
<BR><TT>----------------------</TT><TT></TT>
<P>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.
<P>- Olivier <BR> <BR> </P></BODY></HTML>