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<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Hi Kishore, <o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Thank you very much for your input. It was helpful to clear the
doubts. I am moving ahead with the tracing algorithm.<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Dear users,<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>I am using SymmetricEigenAnalysis filter, code is below. I made
a small observation and would like to share it.<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span style='font-size:10.0pt;
font-family:"Courier New";color:blue'>typedef</span><span style='font-size:
10.0pt;font-family:"Courier New"'> itk::SymmetricEigenAnalysis <
T_PixelType, VectorPixelType, EV_PixelType > EigAnalysisType;<o:p></o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span style='font-size:10.0pt;
font-family:"Courier New"'> EigAnalysisType eig;<o:p></o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span style='font-size:10.0pt;
font-family:"Courier New"'> eig.SetDimension( 3
);<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'> eig.SetOrderEigenMagnitudes(
false );<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>Eigen
value output was :<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>-162.238
16.2334 -829.793<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'> </span><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>eig.SetOrderEigenMagnitudes(
true );<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>Eigen
value output was :<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>16.2334 162.238 -829.793<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>It
is clear that the eigen values and vectors are correctly arranged as per the
increasing order of magnitude, when the parameter is “true”. My
observation was that the last value is still returned in negative. Due to
curiosity i dug inside the code </span><span lang=EN-GB style='font-size:10.0pt;
font-family:Wingdings'>J</span><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'> and found what is the possible reason. This is in
the itkSymmetricEigenAnalysis line 692, code below:<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>else if( m_OrderEigenValues
== OrderByMagnitude )<o:p></o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'> {<o:p></o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'> // Order
by magnitude<o:p></o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New";color:red'> </span><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New";color:#00B050'> </span><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New";color:red'>for (i
= 0; i < m_Order-1; ++i) <o:p></o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>
</span><span style='font-size:10.0pt;font-family:"Courier New"'>{<o:p></o:p></span></p>
<p class=MsoNormal style='text-autospace:none'><span style='font-size:10.0pt;
font-family:"Courier New"'> k = i;<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>
p = d[i];</span><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>I
think instead of “m_Order” , “m_Order – 1” is
used.<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>As
this is the first time i am working with eigen values, i am not sure whether
the magnitude of the eigen will be used for any other calculation. I would like
to know whether this is acceptable or there has to be a change in code.<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>Thank
you,<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>Regards,<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>Kana
<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm'>
<p class=MsoNormal><b><span lang=EN-US style='font-size:10.0pt;font-family:
"Tahoma","sans-serif"'>From:</span></b><span lang=EN-US style='font-size:10.0pt;
font-family:"Tahoma","sans-serif"'> Kishore Mosaliganti
[mailto:kishoreraom@gmail.com] <br>
<b>Sent:</b> 10 March 2010 21:18<br>
<b>To:</b> Arunachalam Kana<br>
<b>Cc:</b> insight-users@itk.org<br>
<b>Subject:</b> Re: [Insight-users] how to calculate point using eigen vector<o:p></o:p></span></p>
</div>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal style='margin-bottom:12.0pt'>Hi Kana,<br>
<br>
You need to arrange the lambda values in the order of decreasing magnitudes. So
based on your convention:<br>
lambda1 = 12.2557<br>
lambda2 = - 560.862<br>
lambda3 = - 1022.66<br>
<br>
You may want to use the filter developed in:<span lang=EN-GB>
"Generalizing vesselness with respect to dimensionality and shape", </span><a
href="http://www.insight-journal.org/browse/publication/175" target="_blank"><span
lang=EN-GB>http://www.insight-journal.org/browse/publication/175</span></a> <br>
The basic work consist of Frangi's measures and it is mentioned in the
references of the above article. Specifically, the above paper implements the
filter proposed by Manniesingh et al.:<br>
"Vessel enhancing diffusion: A scale space representation of vessel
structures "<br>
<br>
This filter will allow you to first preprocess your images and enhance tubes.<br>
<br>
<br>
For your second question, you can follow the center line by looking for the
eigen-vector whose corresponding eigen value has a value closest to 0. The
reason is that along the center-line, there is no gradient in intensity and hence
the lambda1~0. So, you will go in the direction [-0.120 0.010 0.992]<br>
<br>
<br>
<br>
Kishore<br>
<br>
<br>
<o:p></o:p></p>
<div>
<p class=MsoNormal>On Wed, Mar 10, 2010 at 11:31 AM, Arunachalam Kana <<a
href="mailto:Kana.Arunachalam@fh-wels.at">Kana.Arunachalam@fh-wels.at</a>>
wrote:<o:p></o:p></p>
<div>
<div>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>Hi itk users,</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>I am trying to write an algorithm to trace centre line of a tube
shape in 3D CT image.</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>I am using the hessian matrix to get the direction of the tube
shape.</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>The Eigen values and vector of hessian matrix for coordinate
[9,5,2]:</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>Eigen value: -560.862 -1022.66 12.2557 (not in any
order)</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Eigen
vectors: 0.701 0.708 0.078<o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>
-0.702 0.705 -0.092<o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>
-0.120 0.010 0.992<o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>When arranged in |Lambda1| < |Lambda2| < |Lambda3| , i get
12.2557 as Lambda1.</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>If my understanding of literature is right, then the direction of
the tube centre line will</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>point in the direction of eigenvector corresponding to 12.2557 which
is 0.992.</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>If i am right so far, then my question is :</span><o:p></o:p></p>
<p><span lang=EN-GB>1.</span><span lang=EN-GB style='font-size:7.0pt'>
</span><span lang=EN-GB>how to calculate the next coordinate to which i have to
move from [9,5,2]?</span><o:p></o:p></p>
<p><span lang=EN-GB>2.</span><span lang=EN-GB style='font-size:7.0pt'>
</span><span lang=EN-GB>Is there any literature to refer to ?</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>Help to solve this problem will be highly appreciated.</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>Thank you,</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span
lang=EN-GB>Regards,</span><o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Kana<o:p></o:p></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p>
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