Statistics of Nonlinear Spatial Distortions in Histological Images

Local spatial distortions in histological images hinder an exact global registration with corresponding magnetic resonance images (MRI) of the same object. In order to estimate appropriate reference points for an optimized least-square affine transformation matrix, the statistics of deformations is investigated. It is shown, that in the case of correlated and anisotropic histological procedures, local spatial distortions are Rayleigh-Bessel distributed according to the eigenvalues of matrix M describing variance and covariance of the distortions. For uncorrelated, anisotropic procedures, the probablity density function is given by a Rayleigh-Bessel function with corresponding variances and in the case of an uncorrelated and isotropic treatment the density can be described by a Rayleigh function. An advantage of this generalized theory is, that the information about the eigensystem of spatial deformations introduced by angle ϑ can be included in the Rayleigh-Bessel distribution which fits the experimental data more accurately over the entire histogram range and it is not necessary to rotate the images into the eigensystem of M. The application of the theory to histological and corresponding MR images demonstrates an improved registration quality.