The Test of Covariation Functions of Cylindrical and Circular Images

Nowadays, image processing problems are becoming increasingly important due to development of the aerospace Earth monitoring systems, radio and sonar systems, medical devices for early disease diagnosis etc. But the most of the image processing works deal with images defined on rectangular two-dimensional grids or grids of higher dimension. In some practical situations, images are set on a cylinder (for example, images of pipelines, blood vessels, parts during turning) or on a circle (for example, images of the facies (thin film) of dried biological fluid, an eye, cut of a tree trunk). The peculiarity of the domain for specifying such images requires its consideration in their models and processing algorithms. In the present paper, autoregressive models of cylindrical and circular images are considered, and expressions of the correlation function depending on the autoregression parameters are given. The spiral scan of a cylindrical image can be considered as a quasiperiodic process due to the correlation of image rows. To represent inhomogeneous images with random heterogeneity, «doubly stochastic» models are used in which one or more controlling images control the parameters of the resulting image. Given the resulting image, it is possible to estimate parameters of the model of controlling images. But it is not enough to identify hidden images completely. It is necessary to investigate the covariation function of given image. Does it match the hypothetical one? The test for covariation functions of cylindrical and circular images is proposed with investigation its power relative to parameters of image model.