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</o:shapelayout></xml><![endif]--></head><body lang=DE link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Hello,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I try to clarify the both trajectories.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Trajectory 1:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>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<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>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. <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>(Object is not rotating around its own axis).<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Trajectory 2:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>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.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>It’s almost like this trajectory here <a href="https://www.ikeda-shoponline.com/engctsoft/wp-content/uploads/2016/06/Oblique-View-CT1.jpg">https://www.ikeda-shoponline.com/engctsoft/wp-content/uploads/2016/06/Oblique-View-CT1.jpg</a><o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>except that the xray source lies on the rotation axis.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I hope this helps to understand the trajectories I have to deal with.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Kind regards, <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Robert<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span lang=EN-US style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>Von:</span></b><span lang=EN-US style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> simon.rit@gmail.com [mailto:simon.rit@gmail.com] <b>Im Auftrag von </b>Simon Rit<br><b>Gese</b></span><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>ndet:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> Dienstag, 10. Oktober 2017 19:06<br><b>An:</b> Robert Calließ<br><b>Cc:</b> Cyril Mory; rtk-users@public.kitware.com<br><b>Betreff:</b> Re: [Rtk-users] FDK for planar ct<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><div><div><div><div><div><p class=MsoNormal>Hi,<o:p></o:p></p></div><p class=MsoNormal>It's still not clear to me but what is helpful is to think in terms of source trajectory wrt the object.<o:p></o:p></p></div><p class=MsoNormal>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.<o:p></o:p></p></div><p class=MsoNormal>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.<o:p></o:p></p></div><div><p class=MsoNormal>To create the correct geometry, I would suggest using the function <a href="https://github.com/SimonRit/RTK/blob/master/code/rtkThreeDCircularProjectionGeometry.h#L92">AddProjection</a> for which you provide the source and detector positions plus the 3D coordinates of the two axes of the coordinate system of the projection.<o:p></o:p></p></div><p class=MsoNormal>I hope this helps<o:p></o:p></p></div><p class=MsoNormal>Simon<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>On Tue, Oct 10, 2017 at 5:43 PM, "Robert Calließ" <<a href="mailto:Robert.Calliess@gmx.de" target="_blank">Robert.Calliess@gmx.de</a>> wrote:<o:p></o:p></p><div><div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Hello,<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>thank you for the fast reply.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>To answer your questions first.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>In this case the abbrevation pcb stands for printed circuit board.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Next point is the trajectory we are currently handling with.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Please see the attached image "trajectory.png". There are two schematics showing the side view and top view for trajectory type 1<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>and a side-view for trajectory type 2.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>For type 1:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>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.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>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<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>always passes through the centre of the pcb and the centre of the detector.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>For type 2:<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>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<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>around the z-axis.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>I hope this makes clear what trajectory i'm dealing with. Thank you.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Kind regards,<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Robert C.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p></div><div style='border:none;border-left:solid #C3D9E5 1.5pt;padding:0cm 0cm 0cm 8.0pt;margin-left:7.5pt;margin-top:7.5pt;margin-right:3.75pt;margin-bottom:3.75pt;word-wrap:break-word' name=quote><div style='margin-bottom:7.5pt'><p class=MsoNormal><b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Gesendet:</span></b><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> Dienstag, 10. Oktober 2017 um 15:31 Uhr<br><b>Von:</b> "Cyril Mory" <<a href="mailto:cyril.mory@creatis.insa-lyon.fr" target="_blank">cyril.mory@creatis.insa-lyon.fr</a>><br><b>An:</b> "Robert Calliess" <<a href="mailto:robert.calliess@gmx.de" target="_blank">robert.calliess@gmx.de</a>>, <a href="mailto:rtk-users@public.kitware.com" target="_blank">rtk-users@public.kitware.com</a><br><b>Betreff:</b> Re: [Rtk-users] FDK for planar ct<o:p></o:p></span></p></div><div><div><div name=quoted-content><div><p style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Dear Robert,<o:p></o:p></span></p><p style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>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 :<o:p></o:p></span></p><p style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>- what is a PCB ?<o:p></o:p></span></p><p style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>- 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 ?<o:p></o:p></span></p><p style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>- 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 ?<o:p></o:p></span></p><p style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>If you do that, we should have a clear understanding of how your acquisition goes, and be able to give you appropriate advice.<o:p></o:p></span></p><p style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Best regards,<o:p></o:p></span></p><p style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>Cyril<o:p></o:p></span></p><p class=MsoNormal style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p><div><p class=MsoNormal style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'>On 10/10/2017 15:02, Robert Calliess wrote:<o:p></o:p></span></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>Hello rtk users,<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>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.<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>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<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>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<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>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.<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>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<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>rotation (rotation around itself) causes there directional effects.<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>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<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>algorithm for this kind of trajectory ?<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>kind regards,<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;background:white'>Robert C.<o:p></o:p></p></div><p class=MsoNormal style='background:white'><span style='font-size:9.0pt;font-family:"Verdana","sans-serif"'> <o:p></o:p></span></p><pre style='background:white'>_______________________________________________<o:p></o:p></pre><pre style='background:white'>Rtk-users mailing list<o:p></o:p></pre><pre style='background:white'><a href="mailto:Rtk-users@public.kitware.com" target="_blank">Rtk-users@public.kitware.com</a><o:p></o:p></pre><pre style='background:white'><a href="http://public.kitware.com/mailman/listinfo/rtk-users" target="_blank">http://public.kitware.com/mailman/listinfo/rtk-users</a><o:p></o:p></pre></blockquote></div></div></div></div></div></div></div></div><p class=MsoNormal style='margin-bottom:12.0pt'><br>_______________________________________________<br>Rtk-users mailing list<br><a href="mailto:Rtk-users@public.kitware.com">Rtk-users@public.kitware.com</a><br><a href="http://public.kitware.com/mailman/listinfo/rtk-users" target="_blank">http://public.kitware.com/mailman/listinfo/rtk-users</a><o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p></div></div></body></html>