[Rtk-users] distance driven projector, a simplified approach ?

[Robert Calließ]

Hello RTK users,

I guess you know about the distance-driven projector. The main idea,

as far as I understand, of this algorithm is to project voxel boundaries onto

a common plane and the detector cell boundaries also on this common plane.

Then the voxel’s contribution (weight) is the area of this overlapping. I read that the

projection of the voxel and detector cell boundaries on a common plane can be

simplified if the detector is a flat panel detector (guess this is what they called fixed

detector geometry). Even if they  mean by fixed-detector geometry that the detector

is not moving, we could use this simplification in a circular cone beam geometry. We can

either rotate the detector and source around the object or the object can be rotated

and the detector and source are fixed. I think Simon also wrote a paper about the

distance driven projector (?). 

 

 

So my simplified approach would be (fixed detector and source position, object is rotating):

 

a)      project voxel center on detector plane to determine the corresponding detector cell

b)      project voxel vertices on detector plane (dertemine area of this projected polygon)

c)       for each projected voxel vertex dertermine the neares detector cell

o   i.e. vertex(20.3, 10.1) => DetectorCell(20, 10)

d)      dertermine the area of the polygon described by the corresponding detector cells (c)

e)      weight = area_from_b / area_from_d

f)       add voxel_value * weight in detector cell determined in a

 

For the back projector the steps would be always the same (a – e). Value to back project

Is taken from the correction image at position determined in step a.

For step b and d we could determine the minimum bounding rect and use this as the polygons areas.

So the weights should always be between 0 and 1 ( Wether the MEB lies exactly on the detector cells

or in between)

 

I’m new to this topic. I want to hear your opinion. Is this a possible interpretation of the distance-driven

projector, since the main idea is to calculate the overlapping of voxel boundaries with detector cell bounderies.

 

 

Best Regards,

Robert

 

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