[Insight-users] Codimensionality in NarrowBandCurvesLevelSetImageFilter

Tue, 19 Aug 2003 10:27:55 -0400

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Hi,

The work of  Lorigo et al . on codimension-2 level set is based on the
paper of Ambrosio and Soner in order to generalize the mean curvature 
evolution
to arbitrary codimension.
However, evolving curves in 3D images presents numerical problems
because the distance to the curve is always positive and there is no
available fast method to interpolate its position.
For this reason, Lorigo et al.'s evolution is not really codimension-2 
because
 a surface is evolving, but the minimal curvature term that comes from
a codimension-2 evolution allows evolving  better into tubular objects.

Karl Krissian, PhD
Laboratory of Mathematics in Imaging (LMI)
Harvard Medical School, Brigham and Women's Hospital
Tel:617-278-0639, Fax:617-264-6887

Nils Hanssen wrote:

> Hi,
>  
> I just discovered that there is the above image filter in the 
> repository, now. This is quite interesting for me, since I am trying 
> to segment tubular structures in 3D.
>  
> In the paper, the filter is based on, the authors describe that they 
> are fitting an object of codimensionality two (that is a curve instead 
> of a surface) to the dataset. How about the codimensionality in the 
> above filter? Is the filter fitting a curve, too? Or is the 
> codimensionality of the fitting object parameterizable?
>  
> Thanks in advance.
>  
> - Nils
>  
>
> -------------------------
> Nils Hanssen
> Surgical Systems Laboratory
> research center c ae sa r
> Ludwig-Erhard-Allee 2
> 53175 Bonn
> fon: +49-228-9656-197
> fax: +49-228-9656-117
> http://www . caesar . de/ssl
>
>
>  

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Hi, 
 
The work of&nbsp; Lorigo et al . on codimension-2 level set is based on the 
 paper of Ambrosio and Soner in order to generalize the mean curvature evolution 
 to arbitrary codimension. 
 However, evolving curves in 3D images presents numerical problems 
 because the distance to the curve is always positive and there is no 
 available fast method to interpolate its position. 
 For this reason, Lorigo et al.'s evolution is not really codimension-2 because 
 &nbsp;a surface is evolving, but the minimal curvature term that comes from 
 a codimension-2 evolution allows evolving&nbsp; better into tubular objects. 
 
 
Karl Krissian, PhD 
Laboratory of Mathematics in Imaging (LMI) 
Harvard Medical School, Brigham and Women's Hospital 
Tel:617-278-0639, Fax:617-264-6887 
 
 
 
Nils Hanssen wrote: 
<blockquote type="cite" cite="mid000401c3624f$1186ef20$0607010a at ssn4006">

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  <meta content="MSHTML 6.00.2600.0" name="GENERATOR">

  <div><span class="687582510-14082003"><font face="Arial" size="2">Hi,</font></span></div>

  <div><span class="687582510-14082003"></span>&nbsp;</div>

<div>I just
discovered that there is the above image filter in the repository, now.
This is quite interesting for me, since I am trying to segment tubular structures
in 3D.</div>

  <div><span class="687582510-14082003"></span>&nbsp;</div>

<div>In the
paper, the filter is based on, the authors describe that they are fitting
an object of codimensionality two (that is a curve instead of a surface)
to the dataset. How about the codimensionality in the above filter? Is the
filter fitting a curve, too? Or is the codimensionality of the fitting object
 parameterizable?</div>

  <div><span class="687582510-14082003"></span>&nbsp;</div>

  <div><span class="687582510-14082003"><font face="Arial" size="2">Thanks
in  advance.</font></span></div>

  <div><span class="687582510-14082003"></span>&nbsp;</div>

  <div><span class="687582510-14082003"><font face="Arial" size="2">-  Nils</font></span></div>

  <div><span class="687582510-14082003"></span>&nbsp;</div>

------------------------- 
 Nils Hanssen 
 Surgical Systems Laboratory 
 research center c ae sa r 
 Ludwig-Erhard-Allee 2 
 53175 Bonn 
 fon: +49-228-9656-197 
 fax: +49-228-9656-117 
 <a
 href="http://www . caesar . de/ssl" target="_blank">http://www . caesar . de/ssl</a>

  <div>&nbsp;</div>
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