ANALYSIS OF RANDOM POINT IMAGES WITH THE USE OF SYMBOLIC COMPUTATION CODES AND GENERALIZED CATALAN NUMBERS
A. L. Reznik1, A. V. Tuzikov2, A. A. Solov'ev1, A. V. Torgov1
1Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences, prosp. Akademika Koptyuga, 1, Novosibirsk 630090
2United Institute of Informatics Problems, National Academy of Sciences of Belarus, ul. Surganova, 6, Minsk 220012, Belarus
Keywords: случайное изображение, компьютерные аналитические выкладки, обобщённые числа Каталана, случайные компактные группировки, random image, computer analytical calculations, generalized Catalan numbers, random compact groups
Abstract
Original codes and combinatorial-geometrical computational schemes are presented, which are developed and applied for finding exact analytical formulas that describe the probability of error-free readout of random point images recorded by a scanning aperture with a limited number of threshold levels. Combinatorial problems encountered in the course of the study and associated with the new generalization of Catalan numbers are formulated and solved. An attempt is made to find the explicit analytical form of these numbers, which is, on the one hand, a necessary stage of solving the basic research problem and, on the other hand, is an independent self-consistent problem.
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