[Rtk-users] Geometry import and detector displacement

[Notargiacomo Thibault]

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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