  Image registration is the basis for many applications in the fields of
medical image computing and computer assisted interventions. One example is the
registration of 2D X-ray images with preoperative three-dimensional computed
tomography (CT) images in intraoperative surgical guidance systems. Due to the
high safety requirements in medical applications, estimating registration
uncertainty is of a crucial importance in such a scenario. However, previously
proposed methods, including classical iterative registration methods and deep
learning-based methods have one characteristic in common: They lack the
capacity to represent the fact that a registration problem may be inherently
ambiguous, meaning that multiple (substantially different) plausible solutions
exist. To tackle this limitation, we explore the application of invertible
neural networks (INN) as core component of a registration methodology. In the
proposed framework, INNs enable going beyond point estimates as network output
by representing the possible solutions to a registration problem by a
probability distribution that encodes different plausible solutions via
multiple modes. In a first feasibility study, we test the approach for a 2D 3D
registration setting by registering spinal CT volumes to X-ray images. To this
end, we simulate the X-ray images taken by a C-Arm with multiple orientations
using the principle of digitially reconstructed radiographs (DRRs). Due to the
symmetry of human spine, there are potentially multiple substantially different
poses of the C-Arm that can lead to similar projections. The hypothesis of this
work is that the proposed approach is able to identify multiple solutions in
such ambiguous registration problems.
