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Mikko Lilja

Mikko Lilja. Fast and Accurate Voxel Projection Technique in Free-Form Cone-Beam Geometry With Application to Algebraic Reconstruction. Contribution. Projection technique for accelerating analytical object-order raytracing in arbitrary cone-beam geometry

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Mikko Lilja

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

  2. Contribution Projection technique for accelerating analytical object-order raytracing in arbitrary cone-beam geometry Technique’s extension to simultaneous algebraic reconstruction (SART) Similar projection technique independently proposed by N. Li et al. (Computer Physics Communications 178, 2008, p. 518—523)

  3. Digitally reconstructed radiograph • DRR = simulated 2D x-ray image of a 3D image • 2D—3D image registration, computer graphics, tomography reconstruction • Dimensions: 104—107 rays × 106—107 voxels • impossible to store intersections  repeated computation

  4. Proposed projection technique For each image voxel: • Project voxel vertices to detector plane • Determine potentially intersecting rays • Compute ray—voxel intersections • Add voxel’s contribution to DRR

  5. Technique’s application to SART • Computing DRR is computationally equivalent to SART reconstruction: • Iterative update by backprojecting correction DRRs (Kaczmarz technique)

  6. Experiments Compute DRRs from dental CT image (forward problem, projection)‏ Perform SART reconstruction from DRRs (inverse problem, backprojection)‏ Compare reconstruction result to original CT and reconstruction time to clinical CBCT • Programs implemented in Fortran 90

  7. Computing DRRs from CT image 256×256×187 CT, 200 DRRs (310×310), 1.86 s/DRR

  8. Acquired DRR image set 200 DRRs (310×310), pixel size 0.42 mm

  9. SART reconstruction from DRRs 256×256×187 rec, 200 DRRs (310×310), 829.5 s

  10. DRR computation time • 0.23—14.58 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. • 9.64×1011 vs. 4.04×1010 ray—object voxel pairs/sec

  11. SART reconstruction results Precomputation time 3.4—105.8 sec Reconstruction time 50.8—6683.8 sec Clinical applications: 1—6 min Average reconstruction error: 4.52—7.80 (2—3%) Original CT Reconstruction

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

  13. 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

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