Statistics of deformations in histology and application to improved alignment with MRI

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Abstract
An exact registration of magnetic resonance images (MRI) with histological sections is impeded by local deformations resulting from histological preparation procedures. Therefore, it is desirable to know the probability density function of spatial deformations in order to estimate optimal global least-square transformation parameters from suitable landmarks. For this reason, the statistics of deformations is investigated. It is shown analytically that the frequency of occurrence of the absolute geometrical differences (deformations) are Rayleigh-Bessel distributed for anisotropic histological preparation procedures and Rayleigh distributed in the case of isotropic procedures. The probabilistic analysis is given in conjunction with an iterative optimization technique in order to ensure that the probability density function is within a threshold required for the application to experimental data. The application of the analytical model is investigated with real data. It is shown with this data that the extent of deformations varies with the size of the histological section. An individual threshold can be selected on the basis of a Rayleigh-function restricting local corrections to small parts of the image. Thus, global misalignment in each section can be avoided, resulting in an improved 3-D reconstruction of the volume, i.e., the transitions from one section to the next are more continuous.