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Improved C-arm Computed Tomography for the
Early Diagnosis of Osteoarthritis
22.05.2013
Martin Berger
Pattern Recognition Lab, Dept. of Computer Science
Friedrich-Alexander-University Erlangen-Nuremberg
22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Osteoarthritis and Imaging Modalities
● Degeneration of knee cartilage
● Symptoms: pain, stiffness
● Causes: trauma, infection, injury
● Current imaging modalities: MRI, Radiography
● Patient in supine position
● Measure narrowing of joint-space
● Insensitive to early changes
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Taken from: http://www.regenexx.com
Images taken from: www.siemens.com
22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Stress-Test of the Knee Joint
● Measure cartilage deformation under
weight-bearing conditions
● Use C-arm CT with horizontal trajectory
● Patient standing or in squatting position
● Load simulated, e.g. by backpack
● Outcome: deformation vs. load curve
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Reconstruction Challenges
● Limited rotation angle
● Increased patient motion
● Fast scans
low resolution + noise
● Evaluation of the reconstructed
volumes (No ground truth)
Artis Zee MP system
Pros:
• Freely positionable
• Low-priced
Cons:
• Only 160° rotation angle
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Super-Short-Scans
● Iterative methods popular for
reconstructions from few views
● FBP is fast and well known
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𝜆 ≥ 𝜋 + 2𝛿𝑚𝑎𝑥 Short-Scan:
𝜆 < 𝜋 + 2𝛿𝑚𝑎𝑥 Super-Short-Scan: Iterative (TV) New FBP Method
22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Methods
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Redundancy Weights
● Redundant rays
𝑔 𝛿, 𝜆 = 𝑔 −𝛿, 𝜋 + 𝜆 + 2𝛿
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𝜆 ≥ 𝜋 + 2𝛿𝑚𝑎𝑥 Short-Scan:
𝜆 < 𝜋 + 2𝛿𝑚𝑎𝑥 Super-Short-Scan:
22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Compensation Weights
● Scan range: 𝜋 + 𝛿𝑥
● Super-short-scan leads to
missing data
● Compensate missing data by
increasing the weight of spatially
close rays
● Redundancy weights still
needed
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Compensation Weights
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Bilateral Filtering
● Compensation weights can remove low-frequency bias
● Reconstruction still produces streaking artifacts and noise
● Solution: Apply bilateral filter after reconstruction
● Geometric distance: 𝑔1 𝑥′, 𝑦′ = 𝑔 𝑥′, 𝑦′ 𝑇 − 𝑥, 𝑦 𝑇 2, 𝜎𝑔
● Photometric distance: 𝑔2 𝑥′, 𝑦′ = 𝑔( 𝑓 𝑥, 𝑦 − 𝑓 𝑥′, 𝑦′ , 𝜎𝑝)
𝑓𝐵𝐹 𝑥, 𝑦 = 𝑔1 𝑥′, 𝑦′ × 𝑔2(𝑥
′, 𝑦′)
(𝑥′,𝑦′)∈𝑁
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Reconstruction Pipeline
1. Precompute “compensation weights” based on geometry
2. Multiply projection data with “compensation weights”
3. Reconstruct using a conventional FBP approach
4. Apply bilateral filter on reconstructed data
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Evaluation and Results
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Evaluation
● Simulations using the Shepp-Logan phantom
● Geometrical setup
● 640 detector elements of size 0.5mm
● Source to detector distance 500mm
● Fan angle 2𝛿𝑚𝑎𝑥 ≈ 35.5°
● 180 projections in a range of 180° (Short-Scan = 215.5°)
● 5 different reconstructions:
● FBP using redundancy weights
● FBP using redundancy weights + BF
● Iterative with TV regularizer
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● FBP using compensation weights
● FBP using compensation weights + BF
22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Qualitative Results
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Qualitative Results – Line Profiles
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Quantitative Results
● Error metrics:
● Mean-square-error (MSE)
● Relative root mean-square-error (rRMSE)
● Structural similarity index (SSIM)
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rRMSE MSE SSIM
Redundancy 0.1301 0.0286 0.9528
Redundancy BF 0.1271 0.0273 0.9594
Compensation 0.0673 0.0076 0.9594
Compensation BF 0.0569 0.0055 0.9673
Iterative TV 0.0566 0.0054 0.9777
22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Further Results: 160° scan range / 20° fan-angle
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Summary / Outlook
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
Summary / Outlook
● We propose novel projection data weights, that consider:
● redundant data
● missing data
● The weights remove a low-frequency bias caused by missing data
● Bilateral filtering to remove high-frequency artifacts and noise
● Reconstruction results are comparable to iterative, TV regularized
approach
● Future work:
● Extend concept to cone-beam geometry
● Evaluation on real data
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22.05.2013 | Martin Berger | Improved C-arm Computed Tomography for the Early Diagnosis of Osteoarthritis
References
Redundancy Weights
● Parker, D. L. (1982). Optimal short scan convolution reconstruction for fan beam CT. Medical Physics, 9(2), 254–257.
● Silver, M. D. (2000). A method for including redundant data in computed tomography. Medical Physics, 27(4), 773–774.
● Wesarg, S., Ebert, M., & Bortfeld, T. (2002). Parker weights revisited. Medical Physics, 29(3), 372–378.
Super-Short Scan
● Noo, F., Defrise, M., Clackdoyle, R., & Kudo, H. (2002). Image reconstruction from fan-beam projections on less than a short
scan. Physics in medicine and biology, 47(14), 2525–2546.
Iterative vs. FBP
● Bruder, H., Raupach, R., Sunnegardh, J., Sedlmair, M., Stierstorfer, K., & Flohr, T. (2011). Adaptive iterative reconstruction.
Proc. SPIE 7961, Medical Imaging 2011: Physics of Medical Imaging (Vol. 7961, p. 79610J–79610J–12).
● Zeng, G. L. (2012). View-based noise modeling in the filtered backprojection MAP algorithm. Proc. 2nd Intl. Mtg. on image
formation in X-ray CT (pp. 103–106).
● Zeng, G. L., & Zamyatin, A. (2013). A filtered backprojection algorithm with ray-by-ray noise weighting. Medical Physics, 40(3),
031113.
● Zeng, G. L., Li, Y., & Zamyatin, A. (2013). Iterative total-variation reconstruction versus weighted filtered-backprojection
reconstruction with edge-preserving filtering. Physics in Medicine and Biology, 58(10), 3413–3431.
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