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<p class=MsoNormalCxSpFirst><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'>Hi ITK Team and Luis,<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'>To Luis: I am sorry to send a
reply directly to your email instead of <a href="mailto:insight-user@itk.org">insight-user@itk.org</a>.
<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'>Your explanation for
derivative calculation was clear. <o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Gray value at index [8,31,11] = 16951<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Gray value at index [9,31,11] =
20850<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Gray value at index [10,31,11] =
22923<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Gray value at index [11,31,11] =
22923<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Gray value at index [12,31,11] =
20850<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormalCxSpLast><span lang=EN-GB style='font-size:11.0pt;font-family:
"Calibri","sans-serif";color:#1F497D'>My next step was to check whether there Is
any difference in calculating second order derivative using below 2 methods:<o:p></o:p></span></p>
<p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l1 level1 lfo1'><![if !supportLists]><span
lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><span style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'>Using itkDerivativeImagefilter
: set order=2; direction=0; code below<o:p></o:p></span></p>
<p class=MsoNormalCxSpFirst style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DerivativeFilterType::Pointer
DXXfilter = DerivativeFilterType::New();<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXXfilter->SetInput(inputimage);<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXXfilter->SetDirection(0);<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXXfilter->SetOrder(2);<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXXfilter->Update();<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormalCxSpLast style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXX value at [10,31, 11] =
-1036.5<o:p></o:p></span></p>
<p class=MsoListParagraphCxSpFirst style='text-indent:-18.0pt;mso-list:l1 level1 lfo1'><![if !supportLists]><span
lang=EN-GB style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><span style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'>Using
itkDerivativeImagefilter and apply filter 2 time in same direction. Code below<o:p></o:p></span></p>
<p class=MsoListParagraphCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'>DerivativeFilterType::Pointer DXfilter =
DerivativeFilterType::New();<o:p></o:p></span></p>
<p class=MsoListParagraphCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'>DXfilter->SetInput(inputimage);<o:p></o:p></span></p>
<p class=MsoListParagraphCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'>DXfilter->SetDirection(0);<o:p></o:p></span></p>
<p class=MsoListParagraphCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'>DXfilter->SetOrder(1);<o:p></o:p></span></p>
<p class=MsoListParagraphCxSpLast><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'>DXfilter->Update();</span><span lang=EN-GB><o:p></o:p></span></p>
<p class=MsoNormalCxSpFirst style='text-indent:35.4pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DerivativeFilterType::Pointer
DXXfilter = DerivativeFilterType::New();<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:35.4pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXXfilter ->SetInput(DXfilter->GetOutput());<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:35.4pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXXfilter ->SetDirection(0);<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:35.4pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXXfilter ->SetOrder(1);<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:35.4pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXXfilter ->Update();</span><span
lang=EN-GB><o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>DXX value at [10,31, 11] = -502.813
(value is correct as per formula given by Luis in email below)<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>After seeing the result i am
bit confused. Why is there a difference in values between two methods?<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormalCxSpMiddle style='text-indent:17.85pt'><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>Thank you,<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'>Regards,<o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'>Kana <o:p></o:p></span></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormalCxSpMiddle><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=MsoNormalCxSpMiddle><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"'> Luis Ibanez
[mailto:luis.ibanez@kitware.com] <br>
<b>Sent:</b> 16 October 2010 21:39<br>
<b>To:</b> Arunachalam Kana<br>
<b>Cc:</b> insight-users@itk.org<br>
<b>Subject:</b> Re: [Insight-users] Doubt in derivative calculation using
itkDerivativeImageFilter<o:p></o:p></span></p>
</div>
<p class=MsoNormalCxSpMiddle><o:p> </o:p></p>
<p class=MsoNormalCxSpMiddle>Hi Kana,<br>
<br>
It looks like you are not taking the spacing <br>
of the image into account when you compute<br>
the derivatives manually.<br>
<br>
The manual derivative computation should be:<br>
<br>
<span lang=EN-GB> ( 22923 – 20850 ) / (2.0 x spacingAlongX </span>)<br>
<br>
that is:<br>
<br>
f( i+1) - f( i- 1 ) / ( 2 Dx )<br>
<br>
So, I would guess that you image as an<br>
spacing along X that is equal to: 2.0.<br>
<br>
<br>
Regards,<br>
<br>
<br>
Luis<br>
<br>
<br>
------------------------------------------------------------<o:p></o:p></p>
<div>
<p class=MsoNormalCxSpMiddle>On Fri, Oct 15, 2010 at 9:51 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=MsoNormalCxSpMiddle>Dear ITK Users,<o:p></o:p></p>
<p class=MsoNormalCxSpMiddle> <o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>I have a small doubt while I
compare the itkDerivativeImageFilter result with manually calculated
derivative. The code below for itkDerivativeImageFilter:</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New";color:blue'>typedef</span><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>
itk::DerivativeImageFilter<CastImageType,CastImageType>
DerivativeFilterType;</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New"'> </span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB style='font-size:10.0pt;
font-family:"Courier New";color:green'>//create First derivative in X direction</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span style='font-size:10.0pt;font-family:"Courier New"'>DerivativeFilterType::Pointer
DXfilter = DerivativeFilterType::New();</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span style='font-size:10.0pt;font-family:"Courier New"'>DXfilter->SetInput(inputimage);</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span style='font-size:10.0pt;font-family:"Courier New"'>DXfilter->SetDirection(0);</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span style='font-size:10.0pt;font-family:"Courier New"'>DXfilter->SetOrder(1);</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span style='font-size:10.0pt;font-family:"Courier New"'>DXfilter->Update();</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>The following are the grayvalue
of indics:</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Gray value at index [9,31,11] =
20850</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Gray value at index [10,31,11] =
22923</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Gray value at index [11,31,11] =
22923</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Manual calculation of DX at index
[10,31,11] = 22923 – 20850 = 2073</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>The filter calculation of DX at
index [10,31,11] = 518.25 </span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>I have a doubt in how the filter
calculates the derivative. When I read the manual it said “A derivative
at pixel index i = ( j,k), for example, is taken as a weighted</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>difference of the values at (
j+1,k) and ( j</span><span lang=EN-US>−</span><span lang=EN-GB>1,k).” . I would
like to know how is the weighted difference of the values is calculated and is
it ok to calculated the weighted difference ?</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Thank you,</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB> </span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Regards,</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><span lang=EN-GB>Kana Arunachalam Kannappan</span><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle>Research Associate<o:p></o:p></p>
<p class=MsoNormalCxSpMiddle>FH OÖ Forschungs & Entwicklungs GmbH<o:p></o:p></p>
<p class=MsoNormalCxSpMiddle>Stelzhamer Strasse 23,<o:p></o:p></p>
<p class=MsoNormalCxSpMiddle>4600 Wels,<o:p></o:p></p>
<p class=MsoNormalCxSpMiddle>Austria.<o:p></o:p></p>
<p class=MsoNormalCxSpMiddle>Phone: +43 (0)7242 72811 -4420<o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><a href="mailto:kana.arunachalam@fh-wels.at"
target="_blank">kana.arunachalam@fh-wels.at</a><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle><a href="http://www.fh-ooe.at" target="_blank">www.fh-ooe.at</a>;
<a href="http://www.3dct.at" target="_blank">www.3dct.at</a><o:p></o:p></p>
<p class=MsoNormalCxSpMiddle> <o:p></o:p></p>
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