Fast Diffusion Registration

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. 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.