In recent years, new nonlinear partial differential equation (PDE)
based approaches have become popular for solving image processing
problems. Although the outcome of these methods is often very promis-
ing, their actual realization is in general computationally intensive.
Therefore accurate and effcient schemes are needed. The aim of this
paper is two folded. First, we will show that the three dimensional
alignment problem of a histological data set of the human brain may
be phrased in terms of a nonlinear PDE. Second, we will devise a fast
direct solution technique for the associated structured large systems of
linear equations. In addition, the potential of the derived method is
demonstrated on real-life data.