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<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Hi Oleksandr,<o:p></o:p></span></p>
<p class=MsoNormal><span 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 missed this post some time ago. Have you compared by any
chance these results to those of the Discrete Gaussian equivalents so we can also
check their coherency?<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'><a
href="http://www.itk.org/Doxygen316/html/classitk_1_1DiscreteGaussianDerivativeImageFilter.html">http://www.itk.org/Doxygen316/html/classitk_1_1DiscreteGaussianDerivativeImageFilter.html</a>
(and related classes)<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'><a
href="http://www.itk.org/Doxygen316/html/classitk_1_1DiscreteHessianGaussianImageFunction.html">http://www.itk.org/Doxygen316/html/classitk_1_1DiscreteHessianGaussianImageFunction.html</a><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'>Do you have those Gaussian datasets / programs available?<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'>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'>Iván<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'><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"'>
insight-users-bounces@itk.org [mailto:insight-users-bounces@itk.org] <b>En
nombre de </b>Oleksandr Dzyubak<br>
<b>Enviado el:</b> martes, 15 de diciembre de 2009 1:31<br>
<b>Para:</b> Luis Ibanez<br>
<b>CC:</b> insight-users@itk.org<br>
<b>Asunto:</b> Re: [Insight-users] Hessian format for
SymmetricEigenAnalysisImageFilter<o:p></o:p></span></p>
</div>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal style='margin-bottom:12.0pt'><br>
Hi Luis,<br>
<br>
Looks like I am terribly missing something here...<br>
<br>
OK. For my testings I built objects with Gaussian profiles.<br>
These are simple: Gaussian lines with various sigmas extruded <br>
into Z-direction thus I got "Gaussian planes".<br>
Objects: 3D Gaussian planes with Sigma=1,2,3,4,5,10 and intensities I=100.<br>
<br>
Now I use RecursiveGaussians and HessianRecursiveGaussian from the ITK stock
library<br>
and calculate the second order derivative across the Gaussian profiles:<br>
Hxx -- Hessian x-components, Gxx - Gaussian second order derivative,<br>
and GxGx - Gaussian second order derivative taken sequentially as Gx(Gx) <br>
using Gaussian first order derivative.<br>
<br>
Of course, all that was done with "NormalizeAcrossScale" ON and OFF.<br>
Afterwards the maximum of absolute values were measured.<br>
The results I summarized in the table below.<br>
<br>
Sigma ITK_Hxx_OFF
ITK_Gxx_OFF ITK_Hxx_ON
ITK_Gxx_ON ITK_GxGx_OFF ITK_GxGx_ON<br>
<br>
1 35.77
35.77
35.77 35.77
19.47
19.47<br>
2 8.92
8.92
71.33
71.33
4.87
19.47<br>
3
3.96
3.96
106.95 106.95
2.16
19.47<br>
4
2.23
2.23
142.56 142.56
1.22
19.47<br>
5
1.43
1.43
178.18 178.18
0.78
19.47<br>
10
0.36
0.36
356.29 356.29
0.19
19.47<br>
<br>
<br>
As you can see from the table, Hxx is always equal to Gxx for both
"NormalizeAcrossScale" ON and OFF.<br>
Ok. No surprises here. So far so good. <br>
Should not be the values Scale indipendent though?<br>
<br>
Well, now lets take the second order derivative sequentially using Gx(Gx).<br>
Now there is a dramatic difference here.<br>
a) GxGx values do not match Gxx and Hxx anymore.<br>
b) "ITK_GxGx_ON" version apparently demonstrates Scale Space
invariance as it should be.<br>
<br>
<br>
Luis, I would highly appreciate any comments on that.<br>
<br>
Best regards,<br>
<br>
Alex<br>
<br>
<o:p></o:p></p>
<div>
<p class=MsoNormal>On Fri, Dec 11, 2009 at 7:39 PM, Luis Ibanez <<a
href="mailto:luis.ibanez@kitware.com">luis.ibanez@kitware.com</a>> wrote:<o:p></o:p></p>
<p class=MsoNormal>Hi Alex,<br>
<br>
<br>
The order for the Hessian follows the same<br>
pattern of the class<br>
<br>
Insight/Code/Common/<br>
itkSymmetricSecondRankTensor.h<br>
<br>
The elements store only the upper right triangle<br>
of the actual matrix.<br>
<br>
For example, in 3D you get<br>
the following pattern<br>
<br>
0 1 2<br>
3 4<br>
5<br>
<br>
All that to say:<br>
<br>
Yes,<br>
the order that you are using is correct:<br>
<br>
Dxx Dxy
Dxz<br>
Dyy Dyz<br>
Dzz<br>
<br>
<br>
BTW:<br>
You may want to use (or at least look) the filter:<br>
<br>
Insight/Code/BasicFilters/<br>
itkHessianRecursiveGaussianImageFilter.h<br>
<br>
<br>
<br>
Regards,<br>
<br>
<br>
Luis<br>
<br>
<br>
---------------------------------------------------------------<o:p></o:p></p>
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<p class=MsoNormal>On Fri, Dec 11, 2009 at 12:33 PM, Oleksandr Dzyubak <<a
href="mailto:adzyubak@gmail.com">adzyubak@gmail.com</a>> wrote:<br>
><br>
> Dear users,<br>
><br>
> After I built the individual Hessian components,<br>
> in what order should I fill them up to further feed<br>
> into the SymmetricEigenAnalysisImageFilter?<br>
><br>
> At the moment I am using the order below.<br>
><br>
> H[0] = Dxx<br>
> H[1] = Dxy<br>
> H[2] = Dxz<br>
> H[3] = Dyy<br>
> H[4] = Dyz<br>
> H[5] = Dzz<br>
><br>
> Is this correct order?<br>
><br>
> Thanks,<br>
><br>
> Alex<br>
><br>
><o:p></o:p></p>
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