Fast diffusion registration. (English) Zbl 1047.68150

Nashed, M. Zuhair (ed.) et al., Inverse problems, image analysis, and medical imaging. AMS special session on interaction of inverse problems and image analysis, New Orleans, LA, USA, January 10–13, 2001. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2979-3/pbk). Contemp. Math. 313, 117-127 (2002).
Summary: 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.
For the entire collection see [Zbl 1003.00013].


68U10 Computing methodologies for image processing
65F22 Ill-posedness and regularization problems in numerical linear algebra
65F05 Direct numerical methods for linear systems and matrix inversion
68U99 Computing methodologies and applications