The integration of known operators into neural networks has recently received more and
more attention. The theoretical proof of its bene ts has been described by Maier and Syben
et al. in [1, 2]. Reducing the number of trainable weights by replacing trainable layers with
known operators reduces the overall approximation error and makes it easier to interpret
the layers function. This is of special interest in the context of medical imaging, where it is
crucial to understand the e ects of layers or operators on the resulting image. Several use
cases of know operators in medical imaging have been explored in the past few years [3][4][5].
An API to make such experiments easier is the PYRO-NN API by Syben et al. which comes
with several forward and backward projectors for di erent geometries as well as with helpers
such as lters [6].
Cone Beam CT (CBCT) imaging is a widely used X-Ray imaging technology which uses
a point source of X-rays and a 2D at panel detector. Using an reconstruction algorithm
such as the FDK algorithm, a complete 3D reconstruction can be estimated using just one
rotation around the patient [7]. This modality is of great use in orthopedics were so called
weight bearing CT scans image primarily knee joints underweight bearing conditions to
picture the cartilage tissue under stress. The main drawback of this modality are motion
artifacts caused by involuntary movement of the patients knee and inaccuracies in the trajectory
of the scanner. In order to correct those artifacts, the extrinsic camera parameters,
which describe the position and orientation of the object relative to the detector have to be
adjusted [8].
To get one step closer to reduce motion artifacts without additional cameras or markers, it is
of special interest to study the feasibility of training extrinsic camera parameters as part of
a reconstruction pipeline. Before we can assess an algorithm to estimate those parameters,
the general feasibility of training the extrinsic camera parameters of a projection matrix
will be studied. The patients motion will be estimated iterative using a adapted gradient
descent algorithms, known from the training of neural networks.
The Bachelor’s thesis covers the following aspects:
1. Discussing of the general idea of motion compensation in CBCT as well as an quick
overview of the PYRO-NN API and thus into known Operators in general.
2. Study feasibility to learn a projection matrix of a single forward projection:
.Assessing the ability to train single parameters
Training of translations and rotations
Attempt estimate the complete rigid motion parameters
3. Training of a simple trajectory:
Assessing the motion estimation of the back projection using the volume as
ground truth
Assessing the motion estimation using a undistorted sinogram
Estimate the trajectory only based on the distorted sinogram
4. Evaluation of the training results of the experiments and description of potential applications
of the results.
All implementations will be integrated into the PYRO-NN API [6].
References
[1] A. Maier, F. Schebesch, C. Syben, T. Wur , S. Steidl, J. Choi, and R. Fahrig, \Precision
learning: Towards use of known operators in neural networks,” in 2018 24th International
Conference on Pattern Recognition (ICPR), pp. 183{188, 2018.
[2] A. K. Maier, C. Syben, B. Stimpel, T.Wur, M. Ho mann, F. Schebesch, W. Fu, L. Mill,
L. Kling, and S. Christiansen, \Learning with known operators reduces maximum error
bounds,” Nature machine intelligence, vol. 1, no. 8, pp. 373{380, 2019.
[3] W. Fu, K. Breininger, R. Scha ert, N. Ravikumar, T. Wur , J. G. Fujimoto, E. M.
Moult, and A. Maier, \Frangi-Net: A Neural Network Approach to Vessel Segmentation,”
in BildVerarbeitung fur die Medizin (BVM) 2018 (H. H. K. H. M.-H. C. P. T. T.
Andreas Maier, Thomas M. Deserno, ed.), (Berlin, Heidelberg), pp. 341{346, Springer
Vieweg, Berlin, Heidelberg, 2018.
[4] C. Syben, B. Stimpel, K. Breininger, T. Wur , R. Fahrig, A. Dorer, and A. Maier,
\Precision Learning: Reconstruction Filter Kernel Discretization,” in Proceedings of
the 5th International Conference on Image Formation in X-ray Computed Tomography,
pp. 386{390, 2018. UnivIS-Import:2018-09-11:Pub.2018.tech.IMMD.IMMD5.precis 0.
[5] T. Wur , F. C. Ghesu, V. Christlein, and A. Maier, \Deep learning computed tomography,”
in Medical Image Computing and Computer-Assisted Intervention – MICCAI
2016 (S. Ourselin, L. Joskowicz, M. R. Sabuncu, G. Unal, and W. Wells, eds.), (Cham),
pp. 432{440, Springer International Publishing, 2016.
[6] C. Syben, M. Michen, B. Stimpel, S. Seitz, S. Ploner, and A. K. Maier, \Technical note:
Pyro-nn: Python reconstruction operators in neural networks,” Medical Physics, 2019.
[7] L. Feldkamp, L. C. Davis, and J. Kress, \Practical cone-beam algorithm,” J. Opt. Soc.
Am, vol. 1, pp. 612{619, 01 1984.
[8] J. Maier, M. Nitschke, J.-H. Choi, G. Gold, R. Fahrig, B. M. Esko er, and A. Maier,
\Inertial measurements for motion compensation in weight-bearing cone-beam ct of the
knee,” 2020.