[Rtk-users] FDK for planar ct

Tue Oct 10 14:29:00 EDT 2017

Hi,
Let me try to clarify what I mean by "source trajectory wrt the object." In
tomography, you need to determine the source trajectory in the object
coordinate system, we don't really care about the source trajectory in the
room coordinate system. For example, rotating the source on a circular
trajectory or rotating the object makes no difference for the
reconstruction algorithm. That's why we call diagnostic scanners "helical
scanners".
So for trajectory 1, it seems that the source trajectory (again, wrt to the
object) is a circle but the object is offset. This is somewhat similar to
https://doi.org/10.1109/TNS.2006.880977 except that the detector is not
tilted so FDK would be the only FBP algorithm I could think of. But the
situation is really not good, data are missing and iterative reconstruction
should give better results.
Trajectory 2: what I said in my previous email is true, it's useless I
believe, all projections are similar up to a 2D transform of the projection.
Simon

On Tue, Oct 10, 2017 at 8:07 PM, Robert Calliess <robert.calliess at gmx.de>
wrote:

> Hello,
>
> I try to clarify the both trajectories.
>
>
>
> Trajectory 1:
>
> No, i dont move the source on two circles. The xray source is fixed. Only
> the object and the detector moves. Both move on a circular path so that the
> iso-ray
>
> always passes through the pcb centre and the detector centre. There is one
> orthogonal view and the others are the ones moving on the circular path.
>
> (Object is not rotating around its own axis).
>
>
>
> Trajectory 2:
>
> Yes, the xray source lies in the rotation axis and only the object rotates
> around its z-axis. Detector and xray source are fixed and the detector is
> tilted.
>
> It’s almost like this trajectory here https://www.ikeda-shoponline.
> com/engctsoft/wp-content/uploads/2016/06/Oblique-View-CT1.jpg
>
> except that the xray source lies on the rotation axis.
>
>
>
> I hope this helps to understand the trajectories I have to deal with.
>
>
>
> Kind regards,
>
> Robert
>
>
>
>
>
> *Von:* simon.rit at gmail.com [mailto:simon.rit at gmail.com] *Im Auftrag von *Simon
> Rit
> *Gese**ndet:* Dienstag, 10. Oktober 2017 19:06
> *An:* Robert Calließ
> *Cc:* Cyril Mory; rtk-users at public.kitware.com
>
> *Betreff:* Re: [Rtk-users] FDK for planar ct
>
>
>
> Hi,
>
> It's still not clear to me but what is helpful is to think in terms of
> source trajectory wrt the object.
>
> Trajectory 1: if I understand, you move the source on two circles plus one
> point. I don't know of a FBP algorithm to reconstruct this, but there might
> be one. I would consider iterative reconstruction first.
>
> Trajectory 2: your trajectory is a point, the source does not move with
> respect ot the object since it lies on the rotation axis. So each
> projection contains exactly the same information up to a simple 2D
> projection deformation. So it's hopeless to reconstruct from one projection
> only.
>
> To create the correct geometry, I would suggest using the function
> AddProjection
> <https://github.com/SimonRit/RTK/blob/master/code/rtkThreeDCircularProjectionGeometry.h#L92>
> for which you provide the source and detector positions plus the 3D
> coordinates of the two axes of the coordinate system of the projection.
>
> I hope this helps
>
> Simon
>
>
>
> On Tue, Oct 10, 2017 at 5:43 PM, "Robert Calließ" <Robert.Calliess at gmx.de>
> wrote:
>
> Hello,
>
> thank you for the fast reply.
>
> To answer your questions first.
>
> In this case the abbrevation pcb stands for printed circuit board.
>
> Next point is the trajectory we are currently handling with.
>
> Please see the attached image "trajectory.png". There are two schematics
> showing the side view and top view for trajectory type 1
>
> and a side-view for trajectory type 2.
>
>
>
> For type 1:
>
> The xray source is fixed. The pcb is clamped within a transport, so the
> pcb and the detector are moveable with in the xy plane.
>
> As you can see at the image, the pcb moves along a circular path but the
> pcb itself is not rotating. And let's assume that the iso ray
>
> always passes through the centre of the pcb and the centre of the detector.
>
>
>
> For type 2:
>
> The xray source is fixed and the detector is tilted. The pcb lies centred
> in the middle of a table. So that the pcb rotates around its centre
>
> around the z-axis.
>
>
>
>
>
> I hope this makes clear what trajectory i'm dealing with. Thank you.
>
>
>
> Kind regards,
>
> Robert C.
>
>
>
>
>
>
>
>
>
>
>
>
>
> *Gesendet:* Dienstag, 10. Oktober 2017 um 15:31 Uhr
> *Von:* "Cyril Mory" <cyril.mory at creatis.insa-lyon.fr>
> *An:* "Robert Calliess" <robert.calliess at gmx.de>,
> rtk-users at public.kitware.com
> *Betreff:* Re: [Rtk-users] FDK for planar ct
>
> Dear Robert,
>
> Your description of the trajectory is very obscure to me. Maybe you have a
> very unusual X-ray system. Could you make the following points clear :
>
> - what is a PCB ?
>
> - what is fixed/moving in your system (we need this information for the
> object, the source and the detector), and what kind of trajectories have
> the moving parts ?
>
> - can you re-draw your sketch with just 2 or 3 positions (ideally, on
> similar but separate drawings), each one with the object, the source and
> the detector ?
>
> If you do that, we should have a clear understanding of how your
> acquisition goes, and be able to give you appropriate advice.
>
> Best regards,
>
> Cyril
>
>
>
> On 10/10/2017 15:02, Robert Calliess wrote:
>
> Hello rtk users,
>
> I have question to the RTK FDK Filter. As far as I understand from to the
> fourier slice theorem the object to be reconstructed needs a circular
> trajectory and needs to rotate its own centre.
>
> Please have a look at the attached sketch. With this planar trajectory
> (Object, a PCB, is moved on a circle trajectpry  “in-plane”, PCB itself is
> not rotating) do I need
>
> a special filtering if I want to use FDK for planar CT with respect to the
> sketched trajectory ? I tried a circular in-plane trajectory where the PCB
> is centred and rotates
>
> around its centre point. And with 100 projections I get good results. But
> with the trajectory I described (sketch, attached image) the results are
> not so good.
>
> Because of the row-wise ramp filter It looks like there is a directional
> dependency. My assumption is, and with respect to fourier slice theorem,
> that the missing object
>
> rotation (rotation around itself) causes there directional effects.
>
>
>
> So my questions to the experts are. Do I need to apply a special filtering
> before backprojecting with FDK or is it just the wrong
>
> algorithm for this kind of trajectory ?
>
>
>
> kind regards,
>
> Robert C.
>
>
>
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