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.