Matrix Operations on Structural Components of an Image after Topological Decomposition

The problem of dividing an image into structural components is considered in the article. The possibilities of the topological decomposition method for analyzing and processing a set of images from structural components using matrix operations are investigated. It is shown that the algebraic addition of matrices makes it possible to form grouped images, including low-frequency and high-frequency components, according to certain similar topological features. Multiplying the matrix by a number makes it possible to increase the visibility of individual structures in the image, or remove them without affecting the entire image, unlike spectral decomposition methods.