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</o:shapelayout></xml><![endif]--></head><body lang=DE link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Hello RTK users,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I guess you know about the distance-driven projector. The main idea,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>as far as I understand, of this algorithm is to project voxel boundaries onto<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>a common plane and the detector cell boundaries also on this common plane.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Then the voxel’s contribution (weight) is the area of this overlapping. I read that the<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>projection of the voxel and detector cell boundaries on a common plane can be<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>simplified if the detector is a flat panel detector (guess this is what they called fixed<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>detector geometry). Even if they mean by fixed-detector geometry that the detector<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>is not moving, we could use this simplification in a circular cone beam geometry. We can<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>either rotate the detector and source around the object or the object can be rotated<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>and the detector and source are fixed. I think Simon also wrote a paper about the<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>distance driven projector (?). <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>So my simplified approach would be (fixed detector and source position, object is rotating):<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l1 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>a)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>project voxel center on detector plane to determine the corresponding detector cell<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l1 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>b)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>project voxel vertices on detector plane (dertemine area of this projected polygon)<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l1 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>c)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>for each projected voxel vertex dertermine the neares detector cell<o:p></o:p></span></p><p class=MsoListParagraph style='margin-left:72.0pt;text-indent:-18.0pt;mso-list:l1 level2 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Courier New";color:#1F497D'><span style='mso-list:Ignore'>o<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>i.e. vertex(20.3, 10.1) => DetectorCell(20, 10)<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l1 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>d)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>dertermine the area of the polygon described by the corresponding detector cells (c)<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l1 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>e)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>weight = area_from_b / area_from_d<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l1 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>f)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>add voxel_value * weight in detector cell determined in a<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>For the back projector the steps would be always the same (a – e). Value to back project<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Is taken from the correction image at position determined in step a.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>For step b and d we could determine the minimum bounding rect and use this as the polygons areas.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>So the weights should always be between 0 and 1 ( Wether the MEB lies exactly on the detector cells<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>or in between)<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I’m new to this topic. I want to hear your opinion. Is this a possible interpretation of the distance-driven<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>projector, since the main idea is to calculate the overlapping of voxel boundaries with detector cell bounderies.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Best Regards,<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Robert<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p></div></body></html>