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<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>If you simply have a Hessian matrix (SymmetricSecondRankTensor)
you can get the same result by calculating the eigenvalues using the method
ComputeEigenValues(). This is useful for example if you calculate the Hessian
matrix in only a few points and want to calculate corresponding eigenvalues.<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>I don¡¯t know what you understand by ¡°intensity values¡±. In
general, what we call a discrete image is an scalar, vectorial or tensor field
that is sampled in the form a discrete structured grid equispaced along each
direction (that is for every point of the space you get an scalar, vector or
tensor depending on the nature of the field). The values at each grid point can
be scalar (what we usually call intensity) or vectorial (this can be several
values representing for example RGB values, velocity or other magnitudes) or
tensorial (i.e. the Hessian matrix). The scalar need not to be an integer, it
can be for example floating point value and it usually represents the output of
the sensor, a calculated magnitude etc. When you calculate an image of
eigenvalues in fact you get a vector at each point that stores those values
(vector image). You can simply access the value at each point as usual, and since
here you have a vector you may use the array [] operator after accessing the
pixel vector value using iterators (best) or GetPixel() (random access)<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>The EigenValueAccesor in the attached example simply accesses
each component to create three scalar images from the vector image.<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>I hope this answers your questions.<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Best regards <o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Iv¨¢n<o:p></o:p></span></p>
<p class=MsoNormal><span lang=EN-US 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 style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>De:</span></b><span
style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> </span><span
lang=ZH-CN style='font-size:10.0pt'>ËÕÜÛ</span><span style='font-size:10.0pt;
font-family:"Tahoma","sans-serif"'> [mailto:suran.tju@gmail.com] <br>
<b>Enviado el:</b> martes, 29 de junio de 2010 3:28<br>
<b>Para:</b> Ivan Macia<br>
<b>Asunto:</b> Re: [Insight-users] about HessianRecursiveGaussianImageFilter<o:p></o:p></span></p>
</div>
<p class=MsoNormal><o:p> </o:p></p>
<div>
<p class=MsoNormal>Dear Ivan:<o:p></o:p></p>
</div>
<div>
<p class=MsoNormal>Thank you for your answer. <o:p></o:p></p>
</div>
<div>
<p class=MsoNormal>I began to use ITK library very recently.<span
style='font-family:"Calibri","sans-serif"'> </span>I want to compute the
Hessian matrix values and Hessian matrix eigenvalues for linear feature
extraction. <o:p></o:p></p>
</div>
<div>
<p class=MsoNormal>It seems from your answer that the Hessian matrix
eigenvalues after using your code(attachement)<span style='font-family:"Calibri","sans-serif"'> </span>are
not stored as intensity values, then, how can I access these values? <o:p></o:p></p>
</div>
<div>
<p class=MsoNormal>Thanks very much,<span style='font-family:"Calibri","sans-serif"'> </span><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal>Ran<span style='font-family:"Calibri","sans-serif"'> </span><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal>2010/6/29 Ivan Macia <<a
href="mailto:imacia@vicomtech.org" target="_blank">imacia@vicomtech.org</a>><o:p></o:p></p>
<p class=MsoNormal style='margin-bottom:12.0pt'>Hi,<br>
<br>
The Hessian matrix, of type itk::SymmetricSecondRankTensor, is defined in the
filter as a matrix of real values, hence you can store positive and negative
floating point values. This is what you mean?<br>
<br>
Iv<span style='font-family:"Calibri","sans-serif"'>¨¢</span>n<o:p></o:p></p>
<div>
<p class=MsoNormal>2010/6/28 savagegarden <<a
href="mailto:suran.tju@gmail.com" target="_blank">suran.tju@gmail.com</a>><o:p></o:p></p>
<p class=MsoNormal><br>
Hi Iv<span style='font-family:"Calibri","sans-serif"'>¨¢</span>n,<br>
Thank you for your codes.<br>
However, I wonder how you store the Hessian matrix values? If you store as<br>
an image intensity, how you deal with the negative matrix value<span
lang=ZH-CN>£¿</span><br>
Ran<br>
<br>
Iv<span style='font-family:"Calibri","sans-serif"'>¨¢</span>n Mac<span
style='font-family:"Calibri","sans-serif"'>¨ª</span>a wrote:<br>
><br>
> Dear Liu,<br>
><br>
> I made this code based on the Curves3DExtractor application (in<br>
> InsightApplications). It performs eigenanalysis of the Hessian matrix and<br>
> writes 3 images that correspond to the 3 eigenvalues (if nothing is<br>
> wrong).<br>
><br>
> Hope that helps<br>
><br>
> Iv<span style='font-family:"Calibri","sans-serif"'>¨¢</span>n<br>
><br>
> <span style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span>_____<br>
><br>
> De: insight-users-bounces+imacia=<a href="http://vicomtech.es/"
target="_blank">vicomtech.es</a>@<a href="http://itk.org/" target="_blank">itk.org</a><br>
> [mailto:<a href="mailto:insight-users-bounces%2Bimacia" target="_blank">insight-users-bounces+imacia</a>=<a
href="http://vicomtech.es/" target="_blank">vicomtech.es</a>@<a
href="http://itk.org/" target="_blank">itk.org</a>] En nombre de<br>
> SCHMID, Jerome<br>
> Enviado el: jueves, 26 de enero de 2006 2:35<br>
> Para: liu jianfei; ITK<br>
> Asunto: RE: [Insight-users] about HessianRecursiveGaussianImageFilter<br>
><br>
><br>
><br>
> Dear Liu Jianfei,<br>
><br>
> Have a look in the last itk code ( cvs or release ) for the filter<br>
> "itk::Hessian3DToVesselnessMeasureImageFilter" in files<br>
> itkHessian3DToVesselnessMeasureImageFilter.h and<br>
> itkHessian3DToVesselnessMeasureImageFilter.txx. It shows you how to<br>
> perform<br>
> most of the job: compute hessian then eigenvalues and finally compute some<br>
> vesselness measure based on eigenvalues.<br>
><br>
> Best Regards,<br>
><br>
> Jerome Schmid<br>
><br>
> ---------------------------------------------<br>
> Jerome SCHMID<br>
> Project Manager / Engineer<br>
> Augmented and Virtual Reality<br>
> Minimally Invasive Surgical Skills Center (MIS)<br>
> HYPERLINK "<a href="http://www.hkmisc.org.hk/" target="_blank">http://www.hkmisc.org.hk/</a>"<a
href="http://www.hkmisc.org.hk/" target="_blank">http://www.hkmisc.org.hk/</a><br>
> Prince of Wales Hospital<br>
> Chinese University Of Hong-Kong<br>
> ----------------------------------------------<br>
><br>
><br>
><br>
> -----Original Message-----<br>
> From: insight-users-bounces+jeromeschmid=<a
href="http://surgery.cuhk.edu.hk/" target="_blank">surgery.cuhk.edu.hk</a>@<a
href="http://itk.org/" target="_blank">itk.org</a> on<br>
> behalf of liu jianfei<br>
> Sent: Thu 1/26/2006 6:34 AM<br>
> To: ITK<br>
> Subject: [Insight-users] about HessianRecursiveGaussianImageFilter<br>
><br>
><br>
> Hi, everyone<br>
><br>
> <span style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> I've pasted a message
on this class. Just now, I checked that the<br>
> number<br>
> of output is 6 values. They should be the component of the hessian matrix.<br>
> Can someone tell me the order of these values.<br>
> <span style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> Ixx <span
style='font-family:"Calibri","sans-serif"'> </span>Ixy <span
style='font-family:"Calibri","sans-serif"'> </span>Ixz<br>
> <span style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span>Iyy <span
style='font-family:"Calibri","sans-serif"'> </span>Iyz<br>
> <span style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span>Izz<br>
> <span style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> Is the order of these
value Ixx <span style='font-family:"Calibri","sans-serif"'> </span>Ixy <span
style='font-family:"Calibri","sans-serif"'> </span>Ixz Iyy <span
style='font-family:"Calibri","sans-serif"'> </span>Iyz Izz? Thanks<br>
><br>
><br>
> <span style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span> <span
style='font-family:"Calibri","sans-serif"'> </span>Have a nice day!<br>
> --<br>
> Sincerly<br>
> Jianfei Liu<br>
><br>
><br>
> _______________________________________________<br>
> Insight-users mailing list<br>
> <a href="mailto:Insight-users@itk.org" target="_blank">Insight-users@itk.org</a><br>
> HYPERLINK<br>
> "<a href="http://www.itk.org/mailman/listinfo/insight-users"
target="_blank">http://www.itk.org/mailman/listinfo/insight-users</a>"<a
href="http://www.itk.org/mailma" target="_blank">http://www.itk.org/mailma</a><br>
> n/listinfo/insight-users<br>
><br>
><br>
><br>
><br>
> --<br>
> No virus found in this incoming message.<br>
> Checked by AVG Free Edition.<br>
> Version: 7.1.375 / Virus Database: 267.14.21/236 - Release Date:<br>
> 20/01/2006<br>
><br>
><br>
><br>
> --<br>
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><br>
><br>
><br>
> _______________________________________________<br>
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<p class=MsoNormal style='margin-bottom:12.0pt'><br>
<br clear=all>
<br>
-- <br>
Nina(Ran Su)<br>
PhD student<br>
School of Psychiatry<br>
UNSW Randwick Campus<o:p></o:p></p>
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