Abstract: Image registration is one of the most challenging tasks within digital
imaging, in particular in medical imaging. Typically, the underlying problems
are high dimensional and demand for fast and efficient numerical schemes.
Here, we propose a novel scheme for automatic image registration by introducing
a specific regularizing term. The new scheme is called diffusion
registration
since its implementation is based on the solution of a diffusion type partial
differential equation (PDE). The main ingredient for a fast implementation of
the diffusion registration is the so-called additive operator splitting (AOS)
scheme. The AOS-scheme is known to be as accurate as a conventional
semi-implicit scheme and has a linear complexity with respect to the size of
the images. We present a proof of these properties based purely on matrix
analysis.
The performance of the new scheme is demonstrated for a typical medical
registration problem. It is worth noticing that the diffusion registration is
extremely well-suited for a parallel implementation.
Finally, we also draw a connection to Thirion's demon based approach.