[Rtk-users] FDK for planar ct

[Simon Rit]

Hello,
No. The filter should be orthogonal to the rotation axis.  The RTK ramp
filter is along the u axis of the projection.
Trajectory 2: if you take photos by rotating the cameras, they are
photographies of the same point-of-view. This is what I meant.
Cheers,
Simon

On Wed, Oct 11, 2017 at 8:58 PM, Robert Calliess <robert.calliess at gmx.de>
wrote:

> Hello,
>
> thanks for the link to the paper but I dont have access to it. Aside from
> how the trajectory is interpreted within in RTK. My actual question was
>
> if any of those two trajectories would need another reconstruction filter
> than the FDK Filter. From my point of understanding a specific rotation
> around
>
> the object is necessary for fbp/fdk (like c-arm bow, standard circular
> cone-beam trajectory).  That’s why I asked If the first trajectory needs
> some other reconstruction
>
> filter because the object itself doesn’t rotate around itself. It actually
> gets translated on a circular path. So I was more expecting a “yes” or “no”
> to the fdk filter
>
> or a hint to another filter (except iterative reconstructions) I should
> use for these trajectories.
>
>
>
> To trajectory 2: I think the projections are different. The object rotates
> and each projection shows a different view.
>
>
>
>
>
> Kind regards,
>
> Robert C.
>
>
>
> *Von:* simon.rit at gmail.com [mailto:simon.rit at gmail.com] *Im Auftrag von *Simon
> Rit
> *Gesendet:* Dienstag, 10. Oktober 2017 20:29
> *An:* Robert Calliess
>
> *Cc:* Cyril Mory; rtk-users at public.kitware.com
> *Betreff:* Re: [Rtk-users] FDK for planar ct
>
>
>
> 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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