<title>Restoration of three-dimensional quasi-binary images from confocal microscopy and its application to dendritic trees</title>

Abstract

For the analysis of learning processes and the underlying changes of the shape of excitatory synapses (spines), 3-D volume samples of selected dendritic segments are scanned by a confocal laser scanning microscope. For a more detailed analysis, such as the classification of spine types, binary images of higher resolution are required. Simple threshold methods have disadvantages for small structures because the microscope point spread function (PSF) causes a darkening and a spread. The direction-dependent PSF leads to shape errors. To reconstruct structures and edge positions with a resolution smaller than one voxel a parametric model for the dendrite and the spines is created. In our application we use the known tree-like structure of the nerve cell as a- priori information. To create the model, simple geometrical elements (cylinders with hemispheres at the ends) are connected. The model can be adapted for size and position in sub-pixel domain. To estimate the quadratic error between the microscope image and the model, the model is sampled with the same resolution as the microscope image and convolved by the microscope PSF. During an iterative process the parameters of the model are optimized. In contrast to other pixel-based methods. the number of variable parameters is much slower. The influence of small deviations in the microscope image (caused by the inhomogeneous biological materials) is reduced.