[Rtk-users] Physical interpretation of the input and output images when doing a forward projection

[Simon Rit]

Hi Estelle,
Forward projection simply takes the line integrals of your volume. So 3D
images have to represent the physical quantity you want to integrate. For
x-ray imaging, you generally want to have linear attenuation coefficient.
But for PET or SPECT, that would be the emission map in counts per voxel.
In your case, if you want to compute I0*exp(-projection), then it seems
that you're dealing with x-rays and the projection should be the line
integral of the linear attenuation coefficient.
As we point out on the wiki page, integrating HUs makes no physical sense
so you need to convert the input volume or the output projections (since
the operation is linear) before taking the exp.
For the Shepp Logan, be aware that the densities in the text file is to be
understood in the additive sense. So if you have a -0.1 ellipsoid in a
larger 1. ellipsoid, then its density will be 0.9. Use
rtkdrawshepploganphantom to verify what are the actual densities.
Best regards,
Simon

On Fri, Oct 19, 2018 at 2:19 PM MORIN Estelle <estelle.morin at thalesgroup.com>
wrote:

> Dear RTK users,
>
>
>
> I would like to do projections of volumes stored in 3D images. However, I
> do not understand what the voxel values of my 3D images should represent
> physically speaking. Should they represent attenuation coefficients,
> densities or something else? Should they be normalized?
>
>
>
> On the wiki page “RTK/Scripts/ForwardProjection”, it is highlighted that
> the image used for the projection is in Hounsfield units. However,
> computing a projection on the image given in example gives me an output
> image with very high negative values which I can’t interpret. Moreover, as
> the output values are so big and negative, I cannot compute the attenuated
> image with the formula: attenuatedImage = I0 * exp(-projection). Indeed,
> this results in an image with a lot of pixel values equal to infinity.
>
>
>
> I also looked at the file “rtkSheppLoganPhantom.cxx” and its header in
> order to understand what should be my input image. It seems that the Shepp
> Logan Phantom is composed of 10 ellipsoids whose “densities” are included
> in the interval [-1,1]. Moreover, the sum of those densities is equal to
> one. Does this mean that the coefficients of my 3D images should be
> normalized between -1 et 1? What is the physical meaning of this?
>
>
>
> I thank you in advance for your answer,
>
> Best wishes,
>
>
>
> Estelle Morin
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