On the important day, the eleventh of May, I finally defended my dissertation.
The defense was quick and smooth :)
Since this is the end of this story, let me just summarize my work in a nutshell:

The most basic aspect of analysis of grain boundaries is their geometry. With recent development of experimental techniques for three-dimensional (3D) microstructure imaging, it became relatively easy to collect large sets of boundary parameters. This dissertation is devoted to development of effective tools for analysis of such 3D data sets with all five so-called macroscopic boundary parameters taken into consideration. New reliable and fast-to-calculate parameters for recognizing whether a given boundary can be classified as tilt, twist, symmetric, or 180°-tilt are defined. (It is shown that existing solutions are inapplicable to error-affected experimental data or do not take into account crystal symmetry.) Using the new parameters, the frequencies of occurrence of characteristic boundaries are estimated for real materials. A basic characteristic of a boundary network is a distribution of boundaries with respect to their macroscopic parameters. To avoid artifacts caused by the currently used computation method, it is proposed to utilize kernel density estimation (KDE) and to determine boundary distributions based on distance functions defined in the five-dimensional space of boundary parameters. Based on diverse example distributions obtained for several metals, it is shown that with new computational approach, the resulting distributions are clearly more accurate. A scheme of interpretation of the distributions is also proposed. It includes evaluation of their statistical reliability, identification of their symmetries, and verification whether extrema in such distributions correspond to boundaries of characteristic geometry. KDE is also adapted to computation of boundary-plane distributions independent of misorientations. In parallel to developing the abovementioned methods, a package of computer programs including implementations of the new approaches has been created.