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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>If I understood you correct, the input of the Joseph-Filter needs to be oriented in the y-direction when I am dealing with axial oriented slices.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Now I changed the direction of the 3D Slice by rotating it 90 degrees around the x-axis with the itk::ChangeInformationImageFilter to have my slice in the xz-layer in the y-direction:<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> double rotationX = 90;<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> itk::Versor< double > rotation;<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> const double angleInRadians = rotationX * vnl_math::pi / 180.0;<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> rotation.SetRotationAroundX(angleInRadians);<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> const ImageType::DirectionType direction = inputImage->GetDirection();<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> const ImageType::DirectionType newDirection = direction * rotation.GetMatrix();<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> changeFilter->SetOutputDirection(newDirection);<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> changeFilter->ChangeAll();<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> changeFilter->SetInput(inputImage);<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.5pt;font-family:Consolas'> changeFilter->UpdateOutputInformation();</span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Then I added a zero-border as you told me (This changed the size of my region from [512, 512, 1] to [514, 514, 3]).<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>While executing the Joseph Filter I got an error because a vector subscript was out of range. Maybe that’s because the index of the region is [-1,-1,-1] caused by the padding.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>I tried the padding after the Joseph Filter, and got a result which has a size [514, 3, 45], while 45 was the number of projection images but the image was still empty.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>I also tried the Jospeh Filter with a real 3D volume stack of slices, rotated it as described below and got a result.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Now I am confused how I should create the geometry of the Joseph Filter to get a good result.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> typedef rtk::ThreeDCircularProjectionGeometry GeometryType;<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> GeometryType::Pointer geometry = GeometryType::New();<o:p></o:p></span></p><p class=MsoNormal style='text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> for (unsigned int i = 0; i < NumberOfProjectionImages; i++)<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.5pt;font-family:Consolas'> geometry->AddProjection(300., 500., i * 180 / NumberOfProjectionImages);<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:9.5pt;font-family:Consolas'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>I am trying to use a 180-degree rotation, but i don’t have the feeling for the distance values.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>I this code example I used an 3D Image with dimensions = [256, 256, 49]<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>My idea was, since there is no way to get a result with a single 3D slice, I would use a stack of slices as input and slice the output volume in y-direction to get my sinogram as you said.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Tobias<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><b><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Von:</span></b><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'> simon.rit@gmail.com [mailto:simon.rit@gmail.com] <b>Im Auftrag von </b>Simon Rit<br><b>Gesendet:</b> Samstag, 14. Mai 2016 12:17<br><b>An:</b> Tobias Stein <tstein@stud.hs-heilbronn.de><br><b>Cc:</b> rtk-users@public.kitware.com<br><b>Betreff:</b> Re: [Rtk-users] forward and back projection - MITK<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><div><div><div><p class=MsoNormal>The output of the Joseph filter (of any forward projector) is a stack of projection images, i.e., a 3D image. If you slice this 3D image in the z direction, you get one projection images. If you slice this 3D image in the y direction, you get a sinogram, e.g., the 2D sinogram of the central slice (plane of the source trajectory) if y=0. The best way to have this sinogram is to set <span style='font-size:9.5pt;font-family:Consolas'>size[1]=1 </span>and there is no better way to do it in RTK.<o:p></o:p></p></div><p class=MsoNormal>For zero-padding, you need to set extendRegion[?]=1, with (for all dimensions, i.e., ?=0,1,2) and SetConstant(0). I'm surprised though that your image is a black square, something else must be going on. One thing to remember, the typical RTK rotation is around the y axis so your 3D slice must be 1 in the y direction. A simple way to change the orientation of one slice is to change its direction with ChangeImageFilter<o:p></o:p></p></div><p class=MsoNormal>Simon<o:p></o:p></p><div><div><p class=MsoNormal><o:p> </o:p></p></div></div></div><div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>On Sat, May 14, 2016 at 11:48 AM, Tobias Stein <<a href="mailto:tstein@stud.hs-heilbronn.de" target="_blank">tstein@stud.hs-heilbronn.de</a>> wrote:<o:p></o:p></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-right:0cm'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Hello Simon,</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Thanks for your advice so far. I’m getting to know this filter better. At least I can now use it and save the result into a file.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>I updated my code which now uses a volume.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>The values of the input and output volume are equal except of the z-dimension of the output which I changed to the number of projection images.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><span style='font-size:9.5pt;font-family:Consolas'>const unsigned int Dimension = 3;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-indent:36.0pt'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>…Reading image…</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-indent:36.0pt;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'>ImageType::Pointer inputImage = reader->GetOutput();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ImageType::Pointer outputImage = ImageType::New();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> RegionType inputRegion = inputImage->GetLargestPossibleRegion();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> const unsigned int NumberOfProjectionImages = 45;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ImageType::IndexType start;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> start[0] = inputRegion.GetIndex()[0];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> start[1] = inputRegion.GetIndex()[1];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> start[2] = inputRegion.GetIndex()[2];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> RegionType::SizeType size;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> size[0] = inputRegion.GetSize()[0];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> size[1] = inputRegion.GetSize()[1];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> size[2] = NumberOfProjectionImages;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> RegionType region;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> region.SetSize(size);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> region.SetIndex(start);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ImageType::SpacingType spacing;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> spacing[0] = inputImage->GetSpacing()[0];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> spacing[1] = inputImage->GetSpacing()[1];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> spacing[2] = inputImage->GetSpacing()[2];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ImageType::PointType origin;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> origin[0] = inputImage->GetOrigin()[0];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> origin[1] = inputImage->GetOrigin()[1];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> origin[2] = inputImage->GetOrigin()[2];</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> outputImage->SetRegions(region);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> outputImage->SetSpacing(spacing);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> outputImage->SetOrigin(origin);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> outputImage->Allocate();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> outputImage->FillBuffer(size[0] * size[1] * size[2]);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas;color:gainsboro;background:black'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> // Geometry</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> typedef rtk::ThreeDCircularProjectionGeometry GeometryType;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> GeometryType::Pointer geometry = GeometryType::New();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> for (unsigned int i = 0; i < NumberOfProjectionImages; i++)</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> geometry->AddProjection(510., 510., i*8.);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> typedef rtk::JosephForwardProjectionImageFilter<ImageType, ImageType> ForwardType;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ForwardType::Pointer forward = ForwardType::New();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> forward->SetInput(1, inputImage);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> forward->SetInput(0, outputImage);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> forward->SetGeometry(geometry);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> forward->Update();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>I’m not sure how I have to add projection for the geometry to get a result which I’m familiar with.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Can you describe how do I have to interpret the result of the Joseph-Filter? I am familiar with sinograms and how they are computed, but one sinogram is created by the projections of one image slice as far as I understood it. What I want is to manipulate the image in the radon space and then perform a filtered back projection. Typically the articles describe techniques to reduce metal artifacts by using one 2D Slice. Is it possible to achieve something like that with the JosephFilter? I’m guessing since this filter won’t work well for 2D I have to use another filter. Can you give me a hint if I can do something like that with RTK or another ITK-based framework? <a href="https://i.imgur.com/1yBz3o2.png" target="_blank">Here</a> a diagram which shows an example what I want to try.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>I tried also to use my code with one slice and added a zero padding like that:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> typedef itk::ConstantPadImageFilter <ImageType, ImageType> ConstantPadImageFilterType;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ConstantPadImageFilterType::Pointer padFilter = ConstantPadImageFilterType::New();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> padFilter->SetInput(inputImage);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ImageType::SizeType extendRegion;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> extendRegion[0] = 0;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> extendRegion[1] = 0;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> extendRegion[2] = 0;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> padFilter->SetPadLowerBound(extendRegion);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> padFilter->SetPadUpperBound(extendRegion);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> padFilter->SetConstant(1);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> padFilter->Update();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>But the result of my png is a black square.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Tobias</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Von:</span></b><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'> <a href="mailto:simon.rit@gmail.com" target="_blank">simon.rit@gmail.com</a> [mailto:<a href="mailto:simon.rit@gmail.com" target="_blank">simon.rit@gmail.com</a>] <b>Im Auftrag von </b>Simon Rit<br><b>Gesendet:</b> Freitag, 13. </span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Mai 2016 18:15</span><o:p></o:p></p><div><div><p class=MsoNormal><br><b>An:</b> Tobias Stein <<a href="mailto:tstein@stud.hs-heilbronn.de" target="_blank">tstein@stud.hs-heilbronn.de</a>><br><b>Cc:</b> <a href="mailto:rtk-users@public.kitware.com" target="_blank">rtk-users@public.kitware.com</a><br><b>Betreff:</b> Re: [Rtk-users] forward and back projection - MITK<o:p></o:p></p></div></div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Dear Tobias,<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>If you intialize the data of your itk::Image with FillBuffer with the corresponding constant value, it is quite similar. The constant image value allow us to stream the computation whereas you have to allocate the whole image if you pass directly itk::Image.<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>We only work in 3D and probably our projector don't work with 2D, that is probably the problem here. You would have to correct the code for 2D but that's a lot of work, we generally prefer pseudo 2D, see next point.<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>I doubt that our forward projector will work well with one slice only if you use 3D, we assume that the volume starts at the first pixel and ends at the last pixel. You should probably add a zero border around with itk::PadImage to see something.<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>To avoid aliasing, you can cut frequencies in the ramp filter (look for CutFrequency in the doxygen of rtk::FFTRampImageFilter).<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Simon<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Fri, May 13, 2016 at 5:35 PM, Tobias Stein <<a href="mailto:tstein@stud.hs-heilbronn.de" target="_blank">tstein@stud.hs-heilbronn.de</a>> wrote:<o:p></o:p></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Thanks for the information.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>To keep it simple I want to project forward a single slice which I load as a DICOM file.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Now I want to compute the sinogram of that slice and write it in a new file.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>I got a little confused about the ConstantImageSource which is used in the test class. Do I need it to compute a sinogram or is just a replacement of a itk::Image?</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Here is my code so far:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><span style='font-size:9.5pt;font-family:Consolas'>const unsigned int Dimension = 2;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> typedef float PixelType;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> </span><span lang=DE style='font-size:9.5pt;font-family:Consolas'>typedef itk::Image< PixelType, Dimension > ImageType;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>…</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> (reading image by itk::ImageFileReader which works)</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> …</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ImageType::Pointer inputImage = reader->GetOutput();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> const unsigned int NumberOfProjectionImages = 1;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ImageType::Pointer outputImage = ImageType::New();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> typedef rtk::JosephForwardProjectionImageFilter<ImageType, ImageType> ForwardType;</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> ForwardType::Pointer forward = ForwardType::New();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> forward->SetInput(1, inputImage);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> forward->SetInput(0, outputImage);</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> forward->Update();</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-autospace:none'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> …</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> (writing output image into a file)</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> …</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:9.5pt;font-family:Consolas'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>The problem is that I get some errors when I instantiate the forward-Filter.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>The errors are like that one:</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>error C2784: "vnl_matrix<T> operator *(const vnl_diag_matrix<T> &,const vnl_matrix<T> &)": template-Argument für "const vnl_diag_matrix<T> &" konnte nicht von "vnl_matrix_fixed<T,4,4>" hergeleitet werden.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Maybe there is something wrong with the PixelType that i used?</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>If the forward projection works, which filter should i use to achieve a filtered back projection without aliasing?</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Many thanks in advance.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Tobias</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif;color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'><b><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Von:</span></b><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'> </span><a href="mailto:simon.rit@gmail.com" target="_blank"><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>simon.rit@gmail.com</span></a><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'> [mailto:</span><a href="mailto:simon.rit@gmail.com" target="_blank"><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>simon.rit@gmail.com</span></a><span lang=DE style='font-size:11.0pt;font-family:"Calibri",sans-serif'>] <b>Im Auftrag von </b>Simon Rit<br><b>Gesendet:</b> Mittwoch, 4. </span><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>Mai 2016 09:02<br><b>An:</b> Tobias Stein <</span><a href="mailto:tstein@stud.hs-heilbronn.de" target="_blank"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>tstein@stud.hs-heilbronn.de</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>><br><b>Cc:</b> </span><a href="mailto:rtk-users@public.kitware.com" target="_blank"><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>rtk-users@public.kitware.com</span></a><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'><br><b>Betreff:</b> Re: [Rtk-users] forward and back projection - MITK</span><o:p></o:p></p><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><div><div><div><div><div><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Dear Tobias,<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>The forward projection has 2 inputs:<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- input 0: the stack of projections in which you wish to forward project,<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- input 1: the volume you wish to forward project.<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>For the backprojection, it's exactly the same:<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- input 0: the volume in which you wish to backproject,<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>- input 1: the stack of projections you wish to backproject.<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Be aware that JosephBackProjectionImageFilter is the transpose of the forward projection and will have some aliasing (see, e.g., <a href="http://iopscience.iop.org/article/10.1088/0031-9155/49/11/024/meta;jsessionid=87B598ABFDC2AA07D1DED2DEE607F0E7.c2.iopscience.cld.iop.org" target="_blank">De Man and Basu</a> to see what I mean).<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>I have personally never used MITK but don't hesitate to share your experience on the mailing list.<o:p></o:p></p></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Simon<o:p></o:p></p></div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>On Wed, May 4, 2016 at 12:59 AM, Tobias Stein <<a href="mailto:tstein@stud.hs-heilbronn.de" target="_blank">tstein@stud.hs-heilbronn.de</a>> wrote:<o:p></o:p></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0cm 0cm 0cm 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0cm;margin-bottom:5.0pt'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Hi all,<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>i want to use the forward and backward projection to reduce metal artefacts in ct images. I’ve seen so far that I may use the JosephForwardProjectionImageFilter to perform the forward projection. I’ve also seen the test for this class but I don’t get it, where should i put my 2D slice as input to execute the transformation. About the back transformation with the JosephBackProjectionImageFilter I also need more information how I can use it to transform a sinogram back to a ct slice. There is a test at the documentation, but the link is missing there.<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>I’ve got another independent question.<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Are some of you familiar with MITK and know how to get the superbuild up and running with RTK? I am writing a MITK-Plugin and want to reduce the metal artifacts before a segmentation. So if some of you have experience with the combination of RTK and MITK it would be nice if you will share it ;)<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Best regards,<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Tobias<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div></div><p class=MsoNormal style='mso-margin-top-alt:auto;margin-bottom:12.0pt'><br>_______________________________________________<br>Rtk-users mailing list<br><a href="mailto:Rtk-users@public.kitware.com" target="_blank">Rtk-users@public.kitware.com</a><br><a href="http://public.kitware.com/mailman/listinfo/rtk-users" target="_blank">http://public.kitware.com/mailman/listinfo/rtk-users</a><o:p></o:p></p></blockquote></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div></div></div></div></div></blockquote></div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p></div></div></div></div></div></blockquote></div><p class=MsoNormal><o:p> </o:p></p></div></div></body></html>