2026 , Volume 31, № 3, p.107-113

Purpose. The purpose of the conducted research is to solve problems which require identification of anomalies in the analyzed images in the form of local condensations or, conversely, areas with a strong increase in the distances between the nearest elements.

Methodology. A method is proposed for high-speed software calculation of classification features (invariant characteristics) required to identify anomalous condensations or, conversely, fragments with an abnormally large scatter of elements in the analyzed streams of digital point images. The method is based on comparing the characteristics of the processed stream with pre-calculated theoretical standards corresponding to an ensemble of random point images.

The main content. This paper presents standard characteristics (invariants), which describe the probability of the presence of condensations (rarefactions) in a random point image, determined by distances of a given range. Formulas calculated using specialized computer algebra programs are presented. To find particular solutions to the resulting probabilistic problem, an original scheme for equivalently converting the original integral expression to a sum of iterated integrals with predefined integration limits was developed and implemented.

Findings. Using computer algebra and parallel programming tools, new and previously unknown probability dependencies have been obtained that are invariants of a random point image.

Scientific novelty and originality. The originality and scientific novelty of the article simultaneously relies on the results obtained and in the methods developed for its solution. The article presents new probability formulas required for solving problems related to the analysis of random point images.