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    <p>Dear Robert,</p>
    <p>Could you send two datasets of projections, one for each case ?
      We would have a look at them and it would help us understand your
      trajectories. The drawings you sent do not seem to be sufficient
      to remove all ambiguities.<br>
    </p>
    <p>Best regards,</p>
    <p>Cyril<br>
    </p>
    <br>
    <div class="moz-cite-prefix">On 25/10/2017 09:03, "Robert Calließ"
      wrote:<br>
    </div>
    <blockquote type="cite"
cite="mid:trinity-32181a21-bb6b-42aa-9de0-5fcccf241521-1508915009840@3c-app-gmx-bs43">
      <div style="font-family: Verdana;font-size: 12.0px;">
        <div>
          <div>Hello,</div>
          <div>the object is moving on a circular path. There are arrows
            between the different detector positions showing the</div>
          <div>moving direction. The source is static. </div>
          <div> </div>
          <div>Kind regards,</div>
          <div>Robert</div>
          <div> 
            <div style="margin: 10.0px 5.0px 5.0px 10.0px;padding:
              10.0px 0 10.0px 10.0px;border-left: 2.0px solid
              rgb(195,217,229);">
              <div style="margin: 0 0 10.0px 0;"><b>Gesendet:</b> Dienstag,
                24. Oktober 2017 um 16:47 Uhr<br>
                <b>Von:</b> "Simon Rit"
                <a class="moz-txt-link-rfc2396E" href="mailto:simon.rit@creatis.insa-lyon.fr"><simon.rit@creatis.insa-lyon.fr></a><br>
                <b>An:</b> "Robert Calließ"
                <a class="moz-txt-link-rfc2396E" href="mailto:Robert.Calliess@gmx.de"><Robert.Calliess@gmx.de></a><br>
                <b>Cc:</b> <a class="moz-txt-link-rfc2396E" href="mailto:rtk-users@public.kitware.com">"rtk-users@public.kitware.com"</a>
                <a class="moz-txt-link-rfc2396E" href="mailto:rtk-users@public.kitware.com"><rtk-users@public.kitware.com></a><br>
                <b>Betreff:</b> Re: Re: [Rtk-users] FDK for planar ct</div>
              <div>
                <div>
                  <div>
                    <div>Hi,</div>
                    I see one drawing only, not two. And the object does
                    not seem to be moving on your drawing, is it? If not
                    and the source is also static (as it seem), this is
                    equivalent to one large projection.</div>
                  Simon</div>
                <div class="gmail_extra"> 
                  <div class="gmail_quote">On Tue, Oct 24, 2017 at 3:58
                    PM, "Robert Calließ" <span><<a
                        href="mailto:Robert.Calliess@gmx.de"
                        onclick="parent.window.location.href='Robert.Calliess@gmx.de';
                        return false;" target="_blank"
                        moz-do-not-send="true">Robert.Calliess@gmx.de</a>></span>
                    wrote:
                    <blockquote class="gmail_quote" style="margin: 0 0 0
                      0.8ex;border-left: 1.0px rgb(204,204,204)
                      solid;padding-left: 1.0ex;">
                      <div>
                        <div style="font-family: Verdana;font-size:
                          12.0px;">
                          <div>Hello,</div>
                          <div>I suppose there are still
                            misunderstandings with respect to the
                            trajectory.</div>
                          <div>Attached you can find the two difference
                            trajectories. I also had a closer look to</div>
                          <div>the off centered fdk ( the paper you
                            suggested). But I don't think it is in my
                            case.</div>
                          <div>The iso ray passes object center and
                            detector center at each view. Off centered
                            fdk</div>
                          <div>has a different preweighting scheme.</div>
                          <div> </div>
                          <div>You said that the RTK ramp filter is
                            along the u axis (orthogonal to rotaion
                            axis). For planar_ct_1 trajectory that</div>
                          <div>should fit. As you can see at the
                            picture, the object is moving on a circular
                            path but not rotating around the</div>
                          <div>center point (red cross in the image).</div>
                          <div> </div>
                          <div> </div>
                          <div>Kind regards,</div>
                          <div>Robert C.</div>
                          <div> 
                            <div style="margin: 10.0px 5.0px 5.0px
                              10.0px;padding: 10.0px 0 10.0px
                              10.0px;border-left: 2.0px solid
                              rgb(195,217,229);">
                              <div style="margin: 0 0 10.0px 0;"><b>Gesendet:</b> Donnerstag,
                                12. Oktober 2017 um 07:14 Uhr<br>
                                <b>Von:</b> "Simon Rit" <<a
                                  href="mailto:simon.rit@creatis.insa-lyon.fr"
onclick="parent.window.location.href='simon.rit@creatis.insa-lyon.fr';
                                  return false;" target="_blank"
                                  moz-do-not-send="true">simon.rit@creatis.insa-lyon.fr</a>><br>
                                <b>An:</b> "Robert Calliess" <<a
                                  href="mailto:robert.calliess@gmx.de"
                                  onclick="parent.window.location.href='robert.calliess@gmx.de';
                                  return false;" target="_blank"
                                  moz-do-not-send="true">robert.calliess@gmx.de</a>><br>
                                <b>Cc:</b> "<a
                                  href="mailto:rtk-users@public.kitware.com"
onclick="parent.window.location.href='rtk-users@public.kitware.com';
                                  return false;" target="_blank"
                                  moz-do-not-send="true">rtk-users@public.kitware.com</a>"
                                <<a
                                  href="mailto:rtk-users@public.kitware.com"
onclick="parent.window.location.href='rtk-users@public.kitware.com';
                                  return false;" target="_blank"
                                  moz-do-not-send="true">rtk-users@public.kitware.com</a>>
                                <div>
                                  <div class="h5"><br>
                                    <b>Betreff:</b> Re: [Rtk-users] FDK
                                    for planar ct</div>
                                </div>
                              </div>
                              <div>
                                <div class="h5">
                                  <div>
                                    <div>
                                      <div>
                                        <div>
                                          <div>
                                            <div>Hello,</div>
                                            No. The filter should be
                                            orthogonal to the rotation
                                            axis.  The RTK ramp filter
                                            is along the u axis of the
                                            projection.</div>
                                          Trajectory 2: if you take
                                          photos by rotating the
                                          cameras, they are
                                          photographies of the same
                                          point-of-view. This is what I
                                          meant.</div>
                                        Cheers,</div>
                                      Simon</div>
                                    <div class="gmail_extra"> 
                                      <div class="gmail_quote">On Wed,
                                        Oct 11, 2017 at 8:58 PM, Robert
                                        Calliess <span><<a
                                            href="mailto:robert.calliess@gmx.de"
onclick="parent.window.location.href='robert.calliess@gmx.de'; return
                                            false;" target="_blank"
                                            moz-do-not-send="true">robert.calliess@gmx.de</a>></span>
                                        wrote:
                                        <blockquote class="gmail_quote"
                                          style="margin: 0 0 0
                                          0.8ex;border-left: 1.0px
                                          rgb(204,204,204)
                                          solid;padding-left: 1.0ex;">
                                          <div>
                                            <div
                                              class="m_-55466648088813648m_5269510085608132824WordSection1">
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">Hello,</span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">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</span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">if
                                                  any of those two
                                                  trajectories would
                                                  need another
                                                  reconstruction filter
                                                  than the FDK Filter.
                                                  From my point of
                                                  understanding a
                                                  specific rotation
                                                  around</span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">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 </span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">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 </span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">or a
                                                  hint to another filter
                                                  (except iterative
                                                  reconstructions) I
                                                  should use for these
                                                  trajectories.</span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);"> </span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">To
                                                  trajectory 2: I think
                                                  the projections are
                                                  different. The object
                                                  rotates and each
                                                  projection shows a
                                                  different view.</span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);"> </span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);"> </span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">Kind
                                                  regards,</span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);">Robert
                                                  C.</span></p>
                                              <p class="MsoNormal"><span
                                                  style="font-size:
                                                  11.0pt;font-family:
                                                  Calibri ,
                                                  sans-serif;color:
                                                  rgb(31,73,125);"> </span></p>
                                              <p class="MsoNormal"><b><span
                                                    style="font-size:
                                                    10.0pt;font-family:
                                                    Tahoma ,
                                                    sans-serif;">Von:</span></b><span
                                                  style="font-size:
                                                  10.0pt;font-family:
                                                  Tahoma , sans-serif;">
                                                  <a
                                                    href="mailto:simon.rit@gmail.com"
onclick="parent.window.location.href='simon.rit@gmail.com'; return
                                                    false;"
                                                    target="_blank"
                                                    moz-do-not-send="true">simon.rit@gmail.com</a>
                                                  [mailto:<a
                                                    href="mailto:simon.rit@gmail.com"
onclick="parent.window.location.href='simon.rit@gmail.com'; return
                                                    false;"
                                                    target="_blank"
                                                    moz-do-not-send="true">simon.rit@gmail.com</a>]
                                                  <b>Im Auftrag von </b>Simon
                                                  Rit<br>
                                                  <b>Gesendet:</b>
                                                  Dienstag, 1</span><span
                                                  style="font-size:
                                                  10.0pt;font-family:
                                                  Tahoma , sans-serif;">0.
                                                  Oktober 2017 20:29<br>
                                                  <b>An:</b> Robert
                                                  Calliess</span></p>
                                              <div>
                                                <div
                                                  class="m_-55466648088813648h5"><br>
                                                  <b>Cc:</b> Cyril Mory;
                                                  <a
                                                    href="mailto:rtk-users@public.kitware.com"
onclick="parent.window.location.href='rtk-users@public.kitware.com';
                                                    return false;"
                                                    target="_blank"
                                                    moz-do-not-send="true">rtk-users@public.kitware.com</a><br>
                                                  <b>Betreff:</b> Re:
                                                  [Rtk-users] FDK for
                                                  planar ct</div>
                                              </div>
                                              <p> </p>
                                              <div>
                                                <div
                                                  class="m_-55466648088813648h5">
                                                  <p class="MsoNormal"> </p>
                                                  <div>
                                                    <div>
                                                      <div>
                                                        <div>
                                                          <p
                                                          class="MsoNormal">Hi,</p>
                                                        </div>
                                                        <p
                                                          class="MsoNormal">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".</p>
                                                      </div>
                                                      <p
                                                        class="MsoNormal">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 <a
                                                          href="https://doi.org/10.1109/TNS.2006.880977"
target="_blank" moz-do-not-send="true">https://doi.org/10.1109/TNS.2006.880977</a>
                                                        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.</p>
                                                    </div>
                                                    <div>
                                                      <p
                                                        class="MsoNormal">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.</p>
                                                    </div>
                                                    <div>
                                                      <p
                                                        class="MsoNormal">Simon</p>
                                                    </div>
                                                  </div>
                                                  <div>
                                                    <p class="MsoNormal"> </p>
                                                    <div>
                                                      <p
                                                        class="MsoNormal">On
                                                        Tue, Oct 10,
                                                        2017 at 8:07 PM,
                                                        Robert Calliess
                                                        <<a
                                                          href="mailto:robert.calliess@gmx.de"
onclick="parent.window.location.href='robert.calliess@gmx.de'; return
                                                          false;"
                                                          target="_blank"
moz-do-not-send="true">robert.calliess@gmx.de</a>> wrote:</p>
                                                      <div>
                                                        <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">Hello,</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">I
                                                          try to clarify
                                                          the both
                                                          trajectories.</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);"> </span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">Trajectory
                                                          1:</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">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</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">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. </span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">(Object
                                                          is not
                                                          rotating
                                                          around its own
                                                          axis).</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);"> </span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">Trajectory
                                                          2:</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">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.</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">It’s
                                                          almost like
                                                          this
                                                          trajectory
                                                          here <a
href="https://www.ikeda-shoponline.com/engctsoft/wp-content/uploads/2016/06/Oblique-View-CT1.jpg"
target="_blank" moz-do-not-send="true">https://www.ikeda-shoponline.com/engctsoft/wp-content/uploads/2016/06/Oblique-View-CT1.jpg</a></span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">except
                                                          that the xray
                                                          source lies on
                                                          the rotation
                                                          axis.</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);"> </span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">I
                                                          hope this
                                                          helps to
                                                          understand the
                                                          trajectories I
                                                          have to deal
                                                          with.</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);"> </span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">Kind
                                                          regards, </span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);">Robert</span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);"> </span></p>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 11.0pt;font-family: Calibri , sans-serif;color:
                                                          rgb(31,73,125);"> </span></p>
                                                          <p
                                                          class="MsoNormal"><b><span
style="font-size: 10.0pt;font-family: Tahoma , sans-serif;">Von:</span></b><span
style="font-size: 10.0pt;font-family: Tahoma , sans-serif;"> <a
                                                          href="mailto:simon.rit@gmail.com"
onclick="parent.window.location.href='simon.rit@gmail.com'; return
                                                          false;"
                                                          target="_blank"
moz-do-not-send="true">simon.rit@gmail.com</a> [mailto:<a
                                                          href="mailto:simon.rit@gmail.com"
onclick="parent.window.location.href='simon.rit@gmail.com'; return
                                                          false;"
                                                          target="_blank"
moz-do-not-send="true">simon.rit@gmail.com</a>] <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; <a
href="mailto:rtk-users@public.kitware.com"
                                                          onclick="parent.window.location.href='rtk-users@public.kitware.com';
                                                          return false;"
target="_blank" moz-do-not-send="true">rtk-users@public.kitware.com</a></span></p>
                                                          <div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><br>
                                                          <b>Betreff:</b>
                                                          Re:
                                                          [Rtk-users]
                                                          FDK for planar
                                                          ct</p>
                                                          </div>
                                                          </div>
                                                          <div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"> </p>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal">Hi,</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.</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.</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.</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"
target="_blank" moz-do-not-send="true">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.</p>
                                                          </div>
                                                          <p
                                                          class="MsoNormal">I
                                                          hope this
                                                          helps</p>
                                                          </div>
                                                          <p
                                                          class="MsoNormal">Simon</p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"> </p>
                                                          <div>
                                                          <p
                                                          class="MsoNormal">On
                                                          Tue, Oct 10,
                                                          2017 at 5:43
                                                          PM, "Robert
                                                          Calließ" <<a
href="mailto:Robert.Calliess@gmx.de"
                                                          onclick="parent.window.location.href='Robert.Calliess@gmx.de';
                                                          return false;"
target="_blank" moz-do-not-send="true">Robert.Calliess@gmx.de</a>>
                                                          wrote:</p>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">Hello,</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">thank you
                                                          for the fast
                                                          reply.</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">To answer
                                                          your questions
                                                          first.</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.</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.</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</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.</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">For type 1:</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.</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</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.</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">For type 2:</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</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">around the
                                                          z-axis.</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </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.</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">Kind
                                                          regards,</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">Robert C.</span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div>
                                                          <p
                                                          class="MsoNormal"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;"> </span></p>
                                                          </div>
                                                          <div
                                                          style="border:
none;border-left: solid rgb(195,217,229) 1.5pt;padding: 0.0cm 0.0cm
                                                          0.0cm
                                                          8.0pt;margin-left:
7.5pt;margin-top: 7.5pt;margin-right: 3.75pt;margin-bottom: 3.75pt;">
                                                          <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"
onclick="parent.window.location.href='cyril.mory@creatis.insa-lyon.fr';
                                                          return false;"
target="_blank" moz-do-not-send="true">cyril.mory@creatis.insa-lyon.fr</a>><br>
                                                          <b>An:</b> "Robert
                                                          Calliess" <<a
href="mailto:robert.calliess@gmx.de"
                                                          onclick="parent.window.location.href='robert.calliess@gmx.de';
                                                          return false;"
target="_blank" moz-do-not-send="true">robert.calliess@gmx.de</a>>, <a
href="mailto:rtk-users@public.kitware.com"
                                                          onclick="parent.window.location.href='rtk-users@public.kitware.com';
                                                          return false;"
target="_blank" moz-do-not-send="true">rtk-users@public.kitware.com</a><br>
                                                          <b>Betreff:</b> Re:
                                                          [Rtk-users]
                                                          FDK for planar
                                                          ct</span></p>
                                                          </div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <div>
                                                          <p
                                                          style="background:
                                                          white;"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">Dear Robert,</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 :</span></p>
                                                          <p
                                                          style="background:
                                                          white;"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">- what is a
                                                          PCB ?</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 ?</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 ?</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.</span></p>
                                                          <p
                                                          style="background:
                                                          white;"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">Best
                                                          regards,</span></p>
                                                          <p
                                                          style="background:
                                                          white;"><span
style="font-size: 9.0pt;font-family: Verdana , sans-serif;">Cyril</span></p>
                                                          <p
                                                          class="MsoNormal"
style="background: white;"><span style="font-size: 9.0pt;font-family:
                                                          Verdana ,
                                                          sans-serif;"> 
                                                          </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:</span></p>
                                                          </div>
                                                          <blockquote
                                                          style="margin-top:
5.0pt;margin-bottom: 5.0pt;">
                                                          <div>
                                                          <p
                                                          class="MsoNormal"
style="background: white;">Hello rtk users,</p>
                                                          <p
                                                          class="MsoNormal"
style="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.</p>
                                                          <p
                                                          class="MsoNormal"
style="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</p>
                                                          <p
                                                          class="MsoNormal"
style="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</p>
                                                          <p
                                                          class="MsoNormal"
style="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.</p>
                                                          <p
                                                          class="MsoNormal"
style="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</p>
                                                          <p
                                                          class="MsoNormal"
style="background: white;">rotation (rotation around itself) causes
                                                          there
                                                          directional
                                                          effects.</p>
                                                          <p
                                                          class="MsoNormal"
style="background: white;"> </p>
                                                          <p
                                                          class="MsoNormal"
style="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</p>
                                                          <p
                                                          class="MsoNormal"
style="background: white;">algorithm for this kind of trajectory ?</p>
                                                          <p
                                                          class="MsoNormal"
style="background: white;"> </p>
                                                          <p
                                                          class="MsoNormal"
style="background: white;">kind regards,</p>
                                                          <p
                                                          class="MsoNormal"
style="background: white;">Robert C.</p>
                                                          </div>
                                                          <p
                                                          class="MsoNormal"
style="background: white;"><span style="font-size: 9.0pt;font-family:
                                                          Verdana ,
                                                          sans-serif;"> 
                                                              </span></p>
                                                          <pre style="background: white;">_______________________________________________</pre>
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                                                          <p
                                                          class="MsoNormal"
style="margin-bottom: 12.0pt;"><br>
_______________________________________________<br>
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                                                          <p
                                                          class="MsoNormal"> </p>
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      <br>
      <fieldset class="mimeAttachmentHeader"></fieldset>
      <br>
      <pre wrap="">_______________________________________________
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