LAUSR

Imaging problems are becoming increasingly important due to the development of systems for aerospace monitoring of the Earth, radio and sonar location, medical devices for early diagnosis of diseases, etc. However, most of the work on image processing is related to images defined on rectangular two-dimensional grids or grids of higher dimensions. In some practical situations, images are defined on a cylinder (for example, images of pipelines, blood vessels, rotation details) or on a circle (for example, images of a facies (thin film) of dried biological fluid, an eye, a cut of a tree trunk). The specifics of the field of assignment of such images must be taken into account in their models and processing algorithms. In this paper, autoregressive models of cylindrical and circular images are considered and expressions of the correlation function are given depending on the autoregressive parameters. Spiral scanning of a cylindrical image can be viewed as a quasi-periodic process due to the correlation of image lines. To represent heterogeneous images with random heterogeneity, “double stochastic” models are used, in which one or several control images set the parameters of the resulting image. The available image can be used to estimate the parameters of the model of its control images. However, this is not sufficient to fully identify the hidden control images. It is also necessary to evaluate their covariance functions and find out whether they correspond to the hypothetical ones. The paper proposes a test for testing the hypotheses about the covariance functions of cylindrical and circular images with a study of its power relative to the parameters of the image model.