A gradient-based regularization for registration is introduced, and a fast and stable implementation is developed. In contrast to the physically motivated elastic and fluid registrations, the diffusion regularizer is motivated by smoothing properties of the displacement. Another important motivation is that a registration step can be performed in linear complexity of the number of given data. The main tool is the so-called additive operator splitting scheme (AOS). The idea is to split the original problem into a number of simpler problems which allow for a fast numerical solution. A new proof for the accuracy of AOS is given, which is based purely on matrix analysis. Thus, the result also applies to more general situations. Thirion's demons registration is discussed.
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