fast and accurate voxel projection technique in free-form cone-beam geometry with application to...
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Fast and Accurate Voxel Projection Technique in Free-Form Cone-Beam Geometry With Application to Algebraic Reconstruction
Mikko Lilja
Contribution
1. Projection technique for accelerating analytical object-order raytracing in arbitrary cone-beam geometry
2. 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)
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
Proposed projection technique
1. Project voxel vertices to detector plane
2. Determine potentially intersecting rays
3. Compute ray—voxel intersections
4. Add voxel’s contribution to DRR
For each image voxel:
Technique’s application to SART
Computing DRR is computationally equivalent to SART reconstruction:
Iterative update by backprojecting correction DRRs (Kaczmarz technique)
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
Computing DRRs from CT image
256×256×187 CT, 200 DRRs (310×310), 1.86 s/DRR
Acquired DRR image set
200 DRRs (310×310), pixel size 0.42 mm
SART reconstruction from DRRs
256×256×187 rec, 200 DRRs (310×310), 829.5 s
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
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%)
Reconstruction
Original CT
Future work
Validation with clinical x-ray image data
Performance improvement SART
reconstruction in clinical time frame
• Parallelization (HPF / OpenMP)
• GPU computation?
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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