[Rtk-users] Geometry import and detector displacement

[Simon Rit]

Hi Thibault,
It is going to be challenging... but we'll try to do our best to help you.
One important question is: what coordinates system are used by your 3*4
matrices. RTK uses the ITK coordinate system for its images (i.e., the
tomography and the projections), which is defined in ITK by the origin
(coordinate of the center of the first pixel), the spacing, the direction.
Defining this information in your images is very important to have accurate
results. In the DEA.pdf file that you've provided, Fig1.1 shows an origin
of your projectionscoordinate system at the center of the projections, have
you
Your reconstruction example looks indeed completely wrong. Have you tried
to backproject one projection only and to check that it is as expected?
By the way, the AddProjection of the image works in degrees, you should use
AddProjectionInRadians otherwise.
Don't hesitate to share a dataset if you want us to help further.
Simon

On Wed, Dec 3, 2014 at 3:27 PM, Notargiacomo Thibault <gnthibault at gmail.com>
wrote:

> Dear all,
>
> I am currently trying to import data generated with a custom tomographic
> system into RTK, and I am facing issues whith this task.
>
> The system projection matrix is transparently calibrated, and the
> calibration process give a 3*4 projection matrix for each acquisition
> position.
> Each calibration matrix is a direct 3D world to 2D buffer index matrix.
>
> Using the pinhole model, I tried to factorize this matrix as the product
> of various submatrix, including a 3D centered Euler transform, using this
> note <http://staff.city.ac.uk/~sbbh653/publications/euler.pdf> as stated
> in rtkReg23Geometry.cxx.
> The pinhole camera model I used could be find here
> <http://cauchois.iut-amiens.fr/Recherche/Publi/DEA.pdf> at p18 of the pdf.
> I think that the way I factorized the matrix is correct, and match the
> GantryAngle/InPlanAngle/OutOfPlanAngle model described here
> <http://www.openrtk.org/Doxygen/geometry.pdf> .
>
> My problem arise when I try to model the x/z tilt of the detector: when
> decomposing my projection matrix into different matrix, each modelling a
> system coordinate change, I have:
>     - a world coordinate system to source centered system matrix (modeling
> euler 3D rotation and also translation from isocenter to source)
>     - a source centered system to 2D buffer index matrix modeling source
> to detector and pixel size scaling and then detector translation (U0,V0)
>
> As I understand, the pinhole model should allow a perfect fit with the RTK
> geometry model in the following sense:
> Extrinsinc parameters matrix correspond to the SourceTranslationM and
> RotationM in RTK, assuming that the order of the rotation follows RTK
> reference. And the translation in z should be replaced by zero, as it
> correspond to source-isocenter distance, and is taken into accounts in the
> magnification step.
> So I think it is easy to find all the rotation angle, and the sid distance
> as well
>
> Intrinsics parameters matrix could be decomposed in order to find the
> focal (or source detector distance) and the projection offset, from the U0,
> V0 parameters, substracting the detector half size in each direction.
>
> What I do not understand is:
> -In the rtk documentation, it is stated that "The detector position is
> defined with respect to the source" but the ProjectionTranslationM in rtk
> contains a term in sourceOffsetX-projOffsetX although sourceOffset has
> already been taken into account earlier.
> -Why reconstruction aren't working at all
>
> I enclosed you a sample of geometry file I have generated that provide
> some acceptable result when used for phantom projection, but provide
> totally wrong reconstruction when reconstructing my image data with sart
> (sample image taken from a reconstructed volume).
>
> Thank you in advance for you help, and sorry for the long mail
>
>
>
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>
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