[Insight-users] Doubt in derivative calculation using itkDerivativeImageFilter

[Luis Ibanez]

Hi Kana,

I may help to consider that the Derivative operator
is a centered one.

Therefore,

A) When computed First order,
     it uses coefficients

          -0.5,  0.0,   0.5

B) When computed Second order,
     it uses coefficients

          1.0, -2.0, 1.0


  Best,


      Luis


------------------------------------------------------------
On Mon, Oct 18, 2010 at 11:31 AM, Arunachalam Kana <
Kana.Arunachalam at fh-wels.at> wrote:

>  Hi ITK Team and Luis,
>
>
>
> To Luis: I am sorry to send a reply directly to your email instead of
> insight-user at itk.org.
>
>
>
> Your explanation for derivative calculation was clear.
>
> Gray value at index [8,31,11] = 16951
>
> Gray value at index [9,31,11] = 20850
>
> Gray value at index [10,31,11] = 22923
>
> Gray value at index [11,31,11] = 22923
>
> Gray value at index [12,31,11] = 20850
>
>
>
> My next step was to check whether there Is any difference in calculating
> second order derivative using below 2 methods:
>
> 1.       Using  itkDerivativeImagefilter : set order=2; direction=0;  code
> below
>
> DerivativeFilterType::Pointer DXXfilter = DerivativeFilterType::New();
>
> DXXfilter->SetInput(inputimage);
>
> DXXfilter->SetDirection(0);
>
> DXXfilter->SetOrder(2);
>
> DXXfilter->Update();
>
>
>
> DXX value at [10,31, 11] = -1036.5
>
> 2.       Using itkDerivativeImagefilter and apply filter 2 time in same
> direction. Code below
>
> DerivativeFilterType::Pointer DXfilter = DerivativeFilterType::New();
>
> DXfilter->SetInput(inputimage);
>
> DXfilter->SetDirection(0);
>
> DXfilter->SetOrder(1);
>
> DXfilter->Update();
>
> DerivativeFilterType::Pointer DXXfilter = DerivativeFilterType::New();
>
> DXXfilter ->SetInput(DXfilter->GetOutput());
>
> DXXfilter ->SetDirection(0);
>
> DXXfilter ->SetOrder(1);
>
> DXXfilter ->Update();
>
>
>
> DXX value at [10,31, 11] = -502.813 (value is correct as per formula given
> by Luis in email below)
>
>
>
> After seeing the result i am bit confused. Why is there a difference in
> values between two methods?
>
>
>
> Thank you,
>
> Regards,
>
> Kana
>
>
>
>
>
> *From:* Luis Ibanez [mailto:luis.ibanez at kitware.com]
> *Sent:* 16 October 2010 21:39
> *To:* Arunachalam Kana
> *Cc:* insight-users at itk.org
> *Subject:* Re: [Insight-users] Doubt in derivative calculation using
> itkDerivativeImageFilter
>
>
>
> Hi Kana,
>
>
> It looks like you are not taking the spacing
> of the image into account when you compute
> the derivatives manually.
>
> The manual derivative computation should be:
>
>    ( 22923 – 20850 ) / (2.0 x spacingAlongX )
>
> that is:
>
>       f( i+1) - f( i- 1 )  / ( 2 Dx )
>
> So, I would guess that you image as an
> spacing along X that is equal to:   2.0.
>
>
>       Regards,
>
>
>              Luis
>
>
> ------------------------------------------------------------
>
> On Fri, Oct 15, 2010 at 9:51 AM, Arunachalam Kana <
> Kana.Arunachalam at fh-wels.at> wrote:
>
> Dear ITK Users,
>
>
>
> I have a small doubt while I compare the itkDerivativeImageFilter result
> with manually calculated derivative. The code below for
> itkDerivativeImageFilter:
>
> typedef itk::DerivativeImageFilter<CastImageType,CastImageType>
> DerivativeFilterType;
>
>
>
> //create First derivative in X direction
>
> DerivativeFilterType::Pointer DXfilter = DerivativeFilterType::New();
>
> DXfilter->SetInput(inputimage);
>
> DXfilter->SetDirection(0);
>
> DXfilter->SetOrder(1);
>
> DXfilter->Update();
>
>
>
> The following are the grayvalue of indics:
>
> Gray value at index [9,31,11] = 20850
>
> Gray value at index [10,31,11] = 22923
>
> Gray value at index [11,31,11] = 22923
>
>
>
> Manual calculation of DX at index [10,31,11]  = 22923 – 20850 = 2073
>
> The filter calculation of DX at index [10,31,11]  = 518.25
>
>
>
> 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
>
> difference of the values at ( j+1,k) and ( j−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 ?
>
>
>
> Thank you,
>
>
>
> Regards,
>
> Kana Arunachalam Kannappan
>
> Research Associate
>
> FH OÖ Forschungs & Entwicklungs GmbH
>
> Stelzhamer Strasse 23,
>
> 4600 Wels,
>
> Austria.
>
> Phone: +43 (0)7242 72811 -4420
>
> kana.arunachalam at fh-wels.at
>
> www.fh-ooe.at; www.3dct.at
>
>
>
>
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