Abstract
Abstract. The overwhelming majority of known image models are varieties of random fields defined on rectangular two-dimensional grids or grids of higher dimension, for example. In some practical situations, the images have an annular, radial or radial-circular structure. For example, images of the facies (thin film) of dried biological fluid, eyes, cut of a tree trunk or a fruit, blood vessel, erythrocyte, blast pattern, end face detail, etc. In addition, radar and other images are physically obtained in polar or spherical coordinates. These features of images require their consideration in their mathematical models. In this paper, an autoregressive models of homogeneous and inhomogeneous random fields defined on a circle or oval are considered as representations of images with radial or radial-circular structure.
Highlights
The overwhelming majority of known image models are varieties of random fields defined on rectangular twodimensional grids or grids of higher dimension (Duda et al, 2000, Gonzalez et al, 2017, Jähne, 2005, Pratt, 2001)
Radar and other images are physically obtained in polar or spherical coordinates. These features of images require their consideration in random field models, which is necessary for the formulation and solution of problems of processing such images
This paper presented autoregressive models of circular images that have a radial, circular or radial-circular structure
Summary
The overwhelming majority of known image models are varieties of random fields defined on rectangular twodimensional grids or grids of higher dimension (Duda et al, 2000, Gonzalez et al, 2017, Jähne, 2005, Pratt, 2001). Among these models there are autoregressive, polynomial, Gibbs, canonical decompositions, and so on (Gimel’farb, 1999, Soifer, 2009, Vizilter et al, 2015, Woods, 1981).
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