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