  Purpose
  3D acquisitions are often acquired to assess the result in orthopedic trauma
surgery. With a mobile C-Arm system, these acquisitions can be performed
intra-operatively. That reduces the number of required revision surgeries.
However, due to the operation room setup, the acquisitions typically cannot be
performed such that the acquired volumes are aligned to the anatomical regions.
Thus, the multiplanar reconstructed (MPR) planes need to be adjusted manually
during the review of the volume. In this paper, we present a detailed study of
multi-task learning (MTL) regression networks to estimate the parameters of the
MPR planes.
  Approach
  First, various mathematical descriptions for rotation, including Euler angle,
quaternion, and matrix representation, are revised. Then, three different MTL
network architectures based on the PoseNet are compared with a single task
learning network.
  Results
  Using a matrix description rather than the Euler angle description, the
accuracy of the regressed normals improves from $7.7^{\circ}$ to $7.3^{\circ}$
in the mean value for single anatomies. The multi-head approach improves the
regression of the plane position from $7.4mm$ to $6.1mm$, while the orientation
does not benefit from this approach.
  Conclusions
  The results show that a multi-head approach can lead to slightly better
results than the individual tasks networks. The most important benefit of the
MTL approach is that it is a single network for standard plane regression for
all body regions with a reduced number of stored parameters.
