  Registration is widely used in image-guided therapy and image-guided surgery
to estimate spatial correspondences between organs of interest between planning
and treatment images. However, while high-quality computed tomography (CT)
images are often available at planning time, limited angle acquisitions are
frequently used during treatment because of radiation concerns or imaging time
constraints. This requires algorithms to register CT images based on limited
angle acquisitions. We, therefore, formulate a 3D/2D registration approach
which infers a 3D deformation based on measured projections and digitally
reconstructed radiographs of the CT. Most 3D/2D registration approaches use
simple transformation models or require complex mathematical derivations to
formulate the underlying optimization problem. Instead, our approach entirely
relies on differentiable operations which can be combined with modern
computational toolboxes supporting automatic differentiation. This then allows
for rapid prototyping, integration with deep neural networks, and to support a
variety of transformation models including fluid flow models. We demonstrate
our approach for the registration between CT and stationary chest tomosynthesis
(sDCT) images and show how it naturally leads to an iterative image
reconstruction approach.
