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.
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Funding
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project no. AAA-A17-117052410034-6).
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This article is a completely original work of its authors; it has not been published before and will not be sent to other publications until the PRIA Editorial Board decides not to accept it for publication.
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Aleksandr L’vovich Reznik. Born in 1948. Graduated from Novosibirsk State University in 1969. Received Candidate’s degree in 1981. Received Doctoral degree in 2006. Head of Laboratory at the Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences. Scientific interests: analytical and numerical methods for solving complex probabilistic problems usingcomputer technology. Author of more than 100 papers.
Aleksandr Anatol’evich Soloviev. Born in 1980. Graduated from Novosibirsk State University in 2002. Researcher at the Institute of Automation and Electrometry of the Siberian Branch of the Russian Academy of Sciences. Scientific interests: image processing and mathematical statistics. Coauthor of 50 papers.
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Reznik, A.L., Soloviev, A.A. Software and Combinatorial-Probabilistic Tools for the Analysis of Random Point Structures. Pattern Recognit. Image Anal. 32, 636–638 (2022). https://doi.org/10.1134/S1054661822030348
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DOI: https://doi.org/10.1134/S1054661822030348