Abstract

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.

中文翻译：

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检验关于圆柱和圆形图像协方差函数的假设

摘要

由于航空航天监测系统、无线电和声纳定位系统、疾病早期诊断医疗设备等的发展，成像问题变得越来越重要。 然而，大多数图像处理工作都与定义在矩形上的图像有关。二维网格或更高维度的网格。在一些实际情况下，图像被定义在圆柱体上（例如管道、血管、旋转细节的图像）或圆上（例如干燥的生物体液、眼睛、眼睛的相（薄膜）的图像）。砍树干）。在它们的模型和处理算法中必须考虑此类图像分配领域的细节。在本文中，考虑了圆柱和圆形图像的自回归模型，并根据自回归参数给出了相关函数的表达式。由于图像线的相关性，圆柱图像的螺旋扫描可以看作是一个准周期过程。为了表示具有随机异质性的异质图像，使用“双随机”模型，其中一个或多个控制图像设置结果图像的参数。可用图像可用于估计其控制图像的模型参数。然而，这不足以完全识别隐藏的控制图像。还需要评估它们的协方差函数并找出它们是否与假设的函数一致。