  Image registration is a key task in medical imaging applications, allowing to
represent medical images in a common spatial reference frame. Current
approaches to image registration are generally based on the assumption that the
content of the images is usually accessible in clear form, from which the
spatial transformation is subsequently estimated. This common assumption may
not be met in practical applications, since the sensitive nature of medical
images may ultimately require their analysis under privacy constraints,
preventing to openly share the image content.In this work, we formulate the
problem of image registration under a privacy preserving regime, where images
are assumed to be confidential and cannot be disclosed in clear. We derive our
privacy preserving image registration framework by extending classical
registration paradigms to account for advanced cryptographic tools, such as
secure multi-party computation and homomorphic encryption, that enable the
execution of operations without leaking the underlying data. To overcome the
problem of performance and scalability of cryptographic tools in high
dimensions, we propose several techniques to optimize the image registration
operations by using gradient approximations, and by revisiting the use of
homomorphic encryption trough packing, to allow the efficient encryption and
multiplication of large matrices. We demonstrate our privacy preserving
framework in linear and non-linear registration problems, evaluating its
accuracy and scalability with respect to standard, non-private counterparts.
Our results show that privacy preserving image registration is feasible and can
be adopted in sensitive medical imaging applications.
