Intellectual program support for the analysis of random digital images

Abstract

Описаны специализированные методы, разработанные авторами для решения задач обработки случайных точечных изображений, в основе которых лежат построение программных систем для проведения трудоемких аналитических выкладок и использование различных расширений классических чисел Каталана. Приведены примеры эффективного применения предложенных методов для расчета точных аналитических формул, описывающих вероятность безошибочного считывания случайных дискретных полей и цифровых изображений, проводимого сканирующей апертурой с ограниченным числом пороговых уровней. During the digital registration and subsequent processing of fast dynamic processes which have different physical nature, determination for the unknown coordinates of the point-pulse sources becomes one of the most time-consuming and algorithmically complex problems. It happens since it is necessary to satisfy the requirements for accuracy and reliability of registration in such tasks. Finding the exact analytical relationships connecting reliability of the registration with the characteristics of the physical process and the output parameters of the processing system is a problematic and very difficult task in most practically important cases, for example in the case of power of random radiation source and the size of the analyzed field. This paper proposes the methods developed by the authors for calculating the exact analytical formulas and relationships that describe the probability of error-free readout of a random point-pulse field when registration procedure is performed by a scanning aperture with a limited number of threshold levels. The specialized methods, based on the construction of software systems for laborious analytical calculations and the use of various extensions of the classical Catalan numbers are offered. In particular, procedures have been built for multidimensional integration over convex polyhedral areas with freely movable boundaries in n-dimensional space. Two probabilistic problems are also formulated, leading to an extension of the classical Catalan numbers, which turned out to be more convenient to formulate and solve in a symbolic-linguistic form.