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

2. Contribution 1. Projection technique for accelerating analytical object-order raytracing in arbitrary cone-beam geometry 2. Techniques extension to simultaneous algebraic reconstruction (SART) Similar projection technique independently proposed by N. Li et al. (Computer Physics Communications 178, 2008, p. 518523)

3. Digitally reconstructed radiograph DRR = simulated 2D x-ray image of a 3D image 2D3D image registration, computer graphics, tomography reconstruction Dimensions: 10 4 10 7 rays × 10 6 10 7 voxels impossible to store intersections repeated computation

4. Proposed projection technique 1. Project voxel vertices to detector plane 2. Determine potentially intersecting rays 3. Compute rayvoxel intersections 4. Add voxels contribution to DRR For each image voxel:

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

6. 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

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 0.2314.58 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. 9.64×10 11 vs. 4.04×10 10 rayobject voxel pairs/sec

11. 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%) Reconstruction Original CT

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 (t DRR ~ 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