The questions of representation, processing, and analysis of continuous deterministic and random image contours and estimation of their parameters are considered. An approach is proposed to describe continuous complex-valued signals represented on the complex plane in the form of closed contours. A linear space of vector contours is defined and the main analytical relations are obtained.
A model of a random continuous contour is proposed, which is a complex random function. In this case, the complex random function is considered as a set of its possible realizations. The concepts of mathematical expectation and variance of a random contour are introduced. Geometrically, the mathematical expectation of a random contour is interpreted as an “average contour” around which other contours are located: realizations. The dispersion characterizes the degree of scattering of possible realizations (contours) around the mathematical expectation of a random contour (the “middle contour”). It is shown that an important condition for the formation of an adequate contour model with a random form is the equality of the values of the parameters of the linear transformations of the contours of its realizations. Alignment of these parameters should be performed during the formation of a contour model with a random form.
The problems of spectral and correlation analysis of continuous contours are considered and features of their spectra are revealed. The problems of discretization of continuous contours of images are investigated. The structure of the device for processing continuous contours of images and the results of its modeling are presented.
