In applied probability the theory of random sets (stochastic geometry) will be developed; this will lead to new estimators of intrinsic volume densities both in stationary and non-stationary case. The quality of estimators of geometrical characteristics will be described by means of probability distances. The field of probability distances will be improved theoretically, some applications in biology are expected. Stochastic simulations present a complementary tool in stochastic geometry, their development will be directed to random tessellations. Interdisciplinary use of such models will lead to the characterization of the microstructure of nanomaterials. Five PhD students will participate at the solution of the project and an international conference will be organized.
The aim of the project is quantitave evaluation of length density and spatial arrangement of brain microvessels from stacks of optical sections captured by a laser scanning confocal microscope. We will use image enhancement by deconvolution, horizontal and vertical image composition of adjacent fields of view. We will develop and test several methods for capillary detection, measure the length automatically and compare the results with state of art interactive techniques of length measurement. The detection methods will include use of top-hat filters, path extraction methods by minimal path and probabilistic methods using Markov random fields of directions. Spatial arrangement will be characterized by topology, correlation functions, sphere contact distribution function and rose of directions of microvessels.