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Hi Robert,<br>
<br>
I'm glad to know that most of the explanation text is understandable
:)<br>
You might want to check this filter: <br>
<a class="moz-txt-link-freetext" href="http://www.openrtk.org/Doxygen/classrtk_1_1NormalizedJosephBackProjectionImageFilter.html">http://www.openrtk.org/Doxygen/classrtk_1_1NormalizedJosephBackProjectionImageFilter.html</a><br>
You can use the command line application "rtkbackprojections" with
argument --bp to compare "Joseph" and "NormalizedJoseph".<br>
<br>
When performing a back projection with non-normalized Joseph, the
projection values are "splat" (splat is the adjoint operator of
interpolation) between the four nearest voxels in each volume plane
the ray intersects. Nothing guarantees that every voxel will receive
a contribution during this process. How many contributions a voxel
receives is determined by the sampling of the projections, which can
be much looser or much denser (locally and globally) than what would
be required. Dividing by the back projection of an image of ones
mitigates this effect. In theory, as long as the forward and back
projection operators are the adjoint of one another, it should not
be a problem for SART. In practice, it does make a difference.<br>
<br>
I hope it helps. Please let me know if it is still unclear;<br>
<br>
Cyril<br>
<br>
<div class="moz-cite-prefix">On 02/24/2015 09:56 AM, "Robert
Calließ" wrote:<br>
</div>
<blockquote
cite="mid:trinity-f7c85a27-fa92-4445-8f40-616c38c8b007-1424768175348@3capp-gmx-bs52"
type="cite">
<div style="font-family: Verdana;font-size: 12.0px;">
<div>Hello,</div>
<div>in the file rtkSARTConeBeamReconstructionFilter.h there is
briefly written how the</div>
<div>forward and back projection is performed. For the forward
projection, every pixel is</div>
<div>divided by the intersection length of the ray with the
volume. That is clear to me.</div>
<div> </div>
<div>For the back projection applies the following text:</div>
<div>"each voxel of the back projection must be divided by the
value it would take if<br>
a projection filled with ones was being reprojected. This
weighting step is not<br>
performed when using a voxel-based back projection, as the
weights are all equal to one<br>
in this case. When using a ray-based backprojector, typically
Joseph,it must be performed."</div>
<div> </div>
<div>That means a temporary projection image is created where
all pixels have the value "1". So far I understand,</div>
<div>if we use a voxel based back projector we do not need to
apply this weighting step because the ray from source to voxel
center</div>
<div>somewhere hits the detector plane and usually there we
interpolate the pixel value. But all of them are "1" so it's
obsolete to</div>
<div>interpolate inbetween.</div>
<div> </div>
<div>But if we use for instance the joseph back projector don't
we calculate the four weightings at the current volume planes
the</div>
<div>ray intersects with ? So we already have weightings that
range from 0 to 1. I'm a little bit confused about the
projection image</div>
<div>filled with "1". So how a this back projection of "1"
actually happens ?</div>
<div> </div>
<div>I hope someone can help me with that. Thank you.</div>
<div> </div>
<div>best regards,</div>
<div>Robert</div>
<div> </div>
</div>
<br>
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<br>
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