The integration of known operators into neural networks has recently received more and

more attention. The theoretical proof of its benets 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 eects 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 dierent 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. Homann, 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. Schaert, 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. Eskoer, and A. Maier,

\Inertial measurements for motion compensation in weight-bearing cone-beam ct of the

knee,” 2020.