Fast and Accurate Voxel Projection Technique in Free-Form Cone-Beam Geometry With Application to Algebraic Reconstruction

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Fast and Accurate Voxel Projection Technique in
Free-Form Cone-Beam Geometry With Application to
Algebraic Reconstruction

• Mikko Lilja

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Contribution

• Projection technique for accelerating analytical
  object-order raytracing in arbitrary cone-beam
  geometry
• Techniques extension to simultaneous algebraic
  reconstruction (SART)
• Similar projection technique independently
  proposed by N. Li et al. (Computer Physics
  Communications 178, 2008, p. 518523)

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Digitally reconstructed radiograph

• DRR simulated 2D x-ray image of a 3D image
• 2D3D image registration, computer graphics,
  tomography reconstruction
• Dimensions 104107 rays 106107 voxels
• impossible to store intersections ? repeated
  computation

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Proposed projection technique
For each image voxel

1. Project voxel vertices to detector plane
2. Determine potentially intersecting rays
3. Compute rayvoxel intersections
4. Add voxels contribution to DRR

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Techniques application to SART

• Computing DRR is computationally equivalent to
  SART reconstruction

• Iterative update by backprojecting correction
  DRRs (Kaczmarz technique)

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Experiments

1. Compute DRRs from dental CT image (forward
   problem, projection)?
2. Perform SART reconstruction from DRRs (inverse
   problem, backprojection)?
3. Compare reconstruction result to original CT and
   reconstruction time to clinical CBCT

• Programs implemented in Fortran 90

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Computing DRRs from CT image
256256187 CT, 200 DRRs (310310), 1.86 s/DRR
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Acquired DRR image set
200 DRRs (310310), pixel size 0.42 mm
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SART reconstruction from DRRs
256256187 rec, 200 DRRs (310310), 829.5 s
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DRR computation time

• 0.2314.58 sec/DRR
• Performance similar to less accurate DRR
  computation methods
• Direct performance comparison is difficult
  (precomputation time, hardware, etc.)
• Many DRR acceleration techniques are not
  applicable, when volume is updated!
• 24 faster implementation vs. Li et al.
• 9.641011 vs. 4.041010 rayobject voxel pairs/sec

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SART reconstruction results

• Precomputation time 3.4105.8 sec
• Reconstruction time 50.86683.8 sec
• Clinical applications 16 min
• Average reconstruction error 4.527.80 (23)

Original CT
Reconstruction
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Future work

• Validation with clinical x-ray image data
• Performance improvement ? SART reconstruction in
  clinical time frame
• Parallelization (HPF / OpenMP)
• GPU computation?

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Conclusion and acknowlegement

• Advantages
• Speed-up of accurate DRR computation
• Accurate reconstruction in tolerable time with
  excellent scalability (tDRR amount of voxels)
• Flexible and robust implementation
• Drawbacks
• Faster computation needed for clinical
  applications
• Thanks to Martti Kalke at PaloDEx Group Oy
  (Tuusula, Finland) for providing dental image
  material and insight regarding x-ray imaging