Software and Combinatorial-Probabilistic Tools for the Analysis of Random Point Structures
A. L. Reznik, A. A. Soloviev · Pattern Recognition and Image Analysis · 2022
Abstract Approaches to solving problems of processing random point images are described, which are based on the creation of high-performance software systems for carrying out labor-intensive analytical transformations. Original methods for calculating probabilistic relations expressed in the form of multidimensional integral expressions over convex polyhedra in n-dimensional space are implemented in software. A model for transferring the continuous problem of estimating the probability of error-free reading of a random point image into the class of discrete-combinatorial ones is proposed. Using the symbolic-geometric approach, an explicit form of generalized multidimensional Catalan numbers is found.