[Insight-users] Intergral Calculus in ITK

[Luis Ibanez]

Hi John,

Since ITK only deals with discrete images and not with
continuous data, you will have to implement the approximation
to these integrals by using finite difference methods.

For your particular case, you will find useful to look at the
class that computes Digitally Reconstructed Radiographs, since
it uses a similar accumulation (integral) process:

http://www.itk.org/Insight/Doxygen/html/classitk_1_1RayCastInterpolateImageFunction.html

In other words, you approximate the continuous integral by
a discrete sum of elements that are a linear approximation
to the local value of the function.

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You will also find interesting to look at the following paper
in the "Insight Journal":

   http://www.insight-journal.org/browse/publication/177

"Direct Fourier Tomographic Reconstruction Image-To-Image Filter"
by Zosso D., Bach Cuadra M., Thiran J.


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Please let us know if you need help in implementing this filter.
We will be happy to assist you, and we will encourage you to share
it with the community by submitting it to the Insight Journal:
http://www.insight-journal.org



   Regards,


       Luis


----------------------
JOHN ATKINSON wrote:
> Hi,
> I need to know how to implement integral calculus operations  in itk
> for example ∫ Cos (x-α) dα + ∫ Sin α dα .Which category of ITK need to
> be explored so as to perform intergral caluculus operations.I am
> trying to code a pixel specific back projection algorithm which
> corrects respiratory motion artifacts in lung CT.Therefore I need to
> incorporate some integral operatons .Can u please help me.I am using a
> DICOM lung CT data set with artifacts preominantly in the left lung.
> 
> 
> 
> 
> 
> 
> Regards
> 
> John
>